Nonlinear Analysis: Modelling and Control
type: channel
description: Founded in 1997 and dedicated to publishing interdisciplinary works on nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. Indexed in the Scopus (Q2) database since 2009 and in the Web of Science (Q1) database since 2010.
publisher: Vilnius University Press
language: en
publication name: Nonlinear Analysis: Modelling and Control
issn: 1392-5113
copyright: Please read the Copyright Notice in Journal Policy.
items: Comprehensive bifurcation analysis in a delayed epidemic model with media coverage and asymptomatic infection via fractional PD control
items: Global asymptotic synchronization for delayed inertial BAM neural networks without controllers via the fundamental solution matrix method
items: On the dynamics of the autonomous Duffing–Holmes oscillator
items: News-Augmented GARCH model
items: Enhanced chaotic maps for sustainable cryptographic security
items: Computational technique for robust dynamic optimization of fractional impulsive switched systems
items: Joint ruin probability and risk contagion measure in a quota-share reinsurance risk model
items: Positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian
items: Existence of positive solutions for tempered fractional differential equations with p-Laplacian operator
items: Existence and approximate controllability results for time-fractional stochastic Navier–Stokes equations
items: Controllability and Ulam–Hyers stability analysis of conformable fractional differential systems with time delays and impulsive effects
items: Existence, uniqueness and averaging principle for fractional Dirichlet boundary value problems driven by Rosenblatt process and Lévy jumps
items: Fixed-time distributed formation control for nonlinear heterogeneous multiagent systems subject to input nonlinearities and actuator faults
items: Adaptive fixed-time control with prescribed performance for nonlinear networked control systems under deception attacks
items: Synchronization of quaternion-valued BAM neural networks with time-varying delays
items: Evaluation of domain-specific convolutional neural network layers for galaxy classification tasks
items: Adaptive synchronization of quaternion-valued inertial neural networks with uncertain parameters and a flexible time delay
items: Exponential synchronization of quaternion-valued switching neural networks with mixed delays
items: Prescribed-time leader-following scaled consensus for nonlinear multiagent systems
items: An open-source parallel algorithm of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems
items: Entropy generation for MHD pulsating stratified liquid flow between two permeable beds
items: Exact solutions of stochastic generalized long–short wave resonance equations with cubic–quintic nonlinearity via the new sub-ODE method
items: Improved fixed-time consensus of delayed nonlinear leader–follower multi-agent systems
items: Finite-time matrix projective synchronization of fractional-order memristor-based delayed neural networks with parameter uncertainty
items: Stability and stabilization for positive switched delay systems under mode-dependent interval dwell time
items: Adaptive event-triggered output-feedback stabilization for nonlinear systems with function control coefficients
items: Observer-based distributed optimization for linear multiagent systems with external disturbances
items: Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
items: Energetic formulation of the subgroup commutativity degree
items: Nonparametric changed segment detection in functional data

Comprehensive bifurcation analysis in a delayed epidemic model with media coverage and asymptomatic infection via fractional PD control
type: item
description: It is well known that both media coverage and the presence of asymptomatic patients have a significant impact on the spread and control of infectious diseases. Therefore, this paper proposes a class of fractional epidemic models that incorporate media coverage and asymptomatic infection. Also, the time delay for individuals’ response to the current media coverage, as well as the time delay of media coverage, are incorporated in our proposed model to make it more practical. Based on fractional proportional-derivative (PD) control method, Hopf bifurcation is investigated by taking the sum of the two time delays and the order of the fractional derivatives as bifurcation parameters, respectively. Some sufficient delayed-induced and order-induced bifurcation conditions are given. The application and effectiveness of the presented theoretical results are illustrated through a simulation example. Furthermore, the impact of the feedback control gains and the media effect weight on the stability and Hopf bifurcation of the considered epidemic model is explored.
subject: Articles
  topic: section
subject: Hopf bifurcation
  topic: keywords
subject: fractional delayed epidemic model
  topic: keywords
subject: media coverage
  topic: keywords
subject: asymptomatic infection
  topic: keywords
subject: fractional proportional-derivative control
  topic: keywords
creator: Yangling Wang
creator: Jinde Cao
creator: Min Xiao
creator: Lingzhi Zhao
rights: Copyright (c) 2026 Yangling Wang | Jinde Cao | Min Xiao | Lingzhi Zhao https://creativecommons.org/licenses/by/4.0
date: 2026-06-08
publication date: 2026-06-08
starting page: 1
ending page: 21
doi: 10.15388/namc.2026.31.47299

Global asymptotic synchronization for delayed inertial BAM neural networks without controllers via the fundamental solution matrix method
type: item
description: This paper considers the global asymptotic synchronization (GAS) for master-slave delayed inertial bidirectional associative memory (BAM) neural networks (NNs). Most existing studies on GAS rely on the LMI approach, integral inequality, matrix measure, and maximum-valued methods, usually with additional controllers. In contrast, this work achieves GAS without using the above methods or designing any controllers. Instead, two new sufficient conditions are derived via the fundamental solution matrix method for first-order differential systems. For the first time, the fundamental solution matrix method is introduced to deal with the GAS for the NNs.
subject: Articles
  topic: section
subject: master-slave inertial BAM neural networks
  topic: keywords
subject: fundamental solution matrix method
  topic: keywords
subject: global asymptotic synchronization
  topic: keywords
subject: controller-free
  topic: keywords
creator: Yiping Shuai
creator: Zhengqiu Zhang
creator: Zhibin Dai
rights: Copyright (c) 2026 Yiping Shuai | Zhengqiu Zhang | Zhibin Dai https://creativecommons.org/licenses/by/4.0
date: 2026-06-01
publication date: 2026-06-01
starting page: 1
ending page: 25
doi: 10.15388/namc.2026.31.47176

On the dynamics of the autonomous Duffing–Holmes oscillator
type: item
description: The autonomous Duffing–Holmes oscillator ẋ = y, ẏ = x – x3 + by – kz, ż = w(y – z), depending on the three parameters b, k, and w, has been studied previously by several authors who showed that for certain parameter values, it exhibits chaotic motion, or that numerically it has two periodic orbits coming from a Hopf bifurcation, or that it can have three equilibria for some given values of the parameters. Here we provide new results on the integrability and the global dynamics of the autonomous Duffing–Holmes oscillator using its first integrals and Darboux invariants when these exist for some given values of its parameters.
subject: Articles
  topic: section
subject: Duffing–Holmes model
  topic: keywords
subject: first integral
  topic: keywords
subject: rational first integral
  topic: keywords
subject: invariant algebraic surface
  topic: keywords
subject: Darboux invariant
  topic: keywords
creator: Érika Diz-Pita
creator: Jaume Jaume Llibre
creator: M. Victoria Otero-Espinar
rights: Copyright (c) 2026 Érika Diz-Pita | Jaume Jaume Llibre | M. Victoria Otero-Espinar https://creativecommons.org/licenses/by/4.0
date: 2026-05-01
publication date: 2026-05-01
starting page: 699
ending page: 721
doi: 10.15388/namc.2026.31.46613

News-Augmented GARCH model
type: item
description: Volatility is a key measure of financial risk, and GARCH models are widely used to describe its dynamics. However, they do not account for the influence of news sentiment, which can significantly shape market volatility. Recently proposed News-Augmented GARCH model addresses it by incorporating sentiment signals in a nonlinear, asymmetric, and multiplicative form. This paper examines its theoretical properties and performs a simulation-based hyperparameter study. The analysis establishes the existence of a unique and causal solution, derives a stability condition, and evaluates model sensitivity and parameter recovery under controlled scenarios. Results demonstrate robust performance across various settings and provide guidance for informed hyperparameter selection and evaluation, enhancing model’s reliability for empirical applications.
subject: Articles
  topic: section
subject: volatility prediction
  topic: keywords
subject: GARCH
  topic: keywords
subject: news sentiment
  topic: keywords
subject: asymmetry
  topic: keywords
subject: stability condition
  topic: keywords
subject: simulation study
  topic: keywords
creator: Diana Vereškaitė
creator: Jurgita Markevičiūtė
creator: Andrius Buteikis
rights: Copyright (c) 2026 Diana Vereškaitė | Jurgita Markevičiūtė | Andrius Buteikis https://creativecommons.org/licenses/by/4.0
date: 2026-05-26
publication date: 2026-05-26
starting page: 1
ending page: 24
doi: 10.15388/namc.2026.31.47080

Enhanced chaotic maps for sustainable cryptographic security
type: item
description: We propose a comparative study of chaotification techniques that enhance the complexity of one-dimensional maps for sustainable cryptographic applications. Specifically, we examine the use of modulo operation, remainder operation, and k-deep-zoom (k-DZ) transformation applied to the sine map. Each technique’s effectiveness is analyzed using bifurcation diagrams, Lyapunov exponents, and correlation results. Additionally, the statistical performance of the techniques is assessed using the NIST SP 800-22 battery of tests, and the computational efficiency is evaluated in terms of the number of operations. The study aims to identify the best chaotification method for generating robust pseudorandom bit generators (PRBGs) suitable for secure encryption and sustainable cryptography.
subject: Articles
  topic: section
subject: chaotification
  topic: keywords
subject: cryptography
  topic: keywords
subject: Lyapunov exponents
  topic: keywords
subject: NIST tests
  topic: keywords
subject: complexity enhancement
  topic: keywords
creator: Nasr-Eddine Mellah
creator: Samir Ladaci
creator: Murilo S. Baptista
creator: Celso Grebogi
rights: Copyright (c) 2026 Nasr-Eddine Mellah | Samir Ladaci | Murilo S. Baptista | Celso Grebogi https://creativecommons.org/licenses/by/4.0
date: 2026-05-25
publication date: 2026-05-25
starting page: 1
ending page: 12
doi: 10.15388/namc.2026.31.47015

Computational technique for robust dynamic optimization of fractional impulsive switched systems
type: item
description: In this work, we study a robust dynamic optimization problem for nonlinear fractional impulsive switched systems (FISSs) with uncertain parameters. The main novelty lies in directly incorporating parameter sensitivity into the cost functional to enhance robustness against model uncertainty. To solve the resulting problem, the system sensitivity is first computed through an auxiliary FISS, and a time-scaling transformation is employed to reformulate the optimization over fixed switching instants. Tractable gradient expressions are then derived using a set of auxiliary systems. A gradient-based optimization method is subsequently developed to solve the transformed problem together with a numerical scheme tailored for the FISSs. Two numerical examples demonstrate that the proposed technique achieves effective optimization performance and improved robustness.
subject: Articles
  topic: section
subject: fractional impulsive switched system
  topic: keywords
subject: dynamic optimization
  topic: keywords
subject: sensitivity
  topic: keywords
subject: gradient computation
  topic: keywords
subject: numerical technique
  topic: keywords
creator: Zhaohua Gong
creator: Benchawan Wiwatanapataphee
creator: Chongyang Liu
creator: Yonghong Wu
rights: Copyright (c) 2026 Zhaohua Gong | Benchawan Wiwatanapataphee | Chongyang Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
date: 2026-05-15
publication date: 2026-05-15
starting page: 1
ending page: 23
doi: 10.15388/namc.2026.31.46903

Joint ruin probability and risk contagion measure in a quota-share reinsurance risk model
type: item
description: Consider a quota-share reinsurance risk model with constant premiums and stochastic returns in which an insurer purchases fixed-proportion quota-share reinsurance for its business line. Both the insurer and reinsurer may engage in risk-free investments, with their nonnegative general (not necessarily Lévy) log-price processes following an arbitrary dependence structure. Under the assumption that claim sizes are pairwise strongly quasiasymptotically independent and follow heavy-tailed distributions, this paper derives asymptotic formulas for two types of finite-time joint ruin probabilities and for a risk contagion measure from the insurer to the reinsurer. Furthermore, we conduct numerical studies to verify the accuracy of the derived asymptotic results, using the Monte Carlo method combined with an explicit order-3.0 weak scheme.
subject: Articles
  topic: section
subject: asymptotics
  topic: keywords
subject: quota-share reinsurance risk model
  topic: keywords
subject: finite-time joint ruin probability
  topic: keywords
subject: risk contagion measure
  topic: keywords
subject: explicit order-3.0 weak scheme
  topic: keywords
creator: Yang Yang
creator: Rongshan Huang
creator: Hui Meng
rights: Copyright (c) 2026 Yang Yang | Rongshan Huang | Hui Meng https://creativecommons.org/licenses/by/4.0
date: 2026-05-11
publication date: 2026-05-11
starting page: 1
ending page: 22
doi: 10.15388/namc.2026.31.46812

Positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian
type: item
description: In this paper, we investigate the existence of positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian operator. First, we construct a linear operator that incorporates impulsive effects, and then analyze its spectral radius properties. Subsequently, under suitable conditions on the spectral radius, we apply the fixed point index theory to establish existence theorems for the problem. Our results cover cases where the nonlinear term exhibits (p – 1)-superlinear/sublinear growth, and the impulsive term satisfies superlinear/sublinear growth conditions.
subject: Articles
  topic: section
subject: fourth-order integral boundary value problem
  topic: keywords
subject: positive solutions
  topic: keywords
subject: fixed point index
  topic: keywords
creator: Jiafa Xu
creator: Zhichun Yang
creator: Donal O’Regan
creator: Jiangdong Liao
rights: Copyright (c) 2026 Jiafa Xu | Zhichun Yang | Donal O’Regan | Jiangdong Liao https://creativecommons.org/licenses/by/4.0
date: 2026-04-28
publication date: 2026-04-28
starting page: 1
ending page: 25
doi: 10.15388/namc.2026.31.46559

Existence of positive solutions for tempered fractional differential equations with p-Laplacian operator
type: item
description: This paper investigates the existence of positive solutions for a specific category of p-Laplacian tempered fractional differential equations in which the nonlinear term f contains an integral operator θ. By employing fixed point theorems for sum operators in partially ordered Banach spaces, together with Krasnosel’skii fixed point theorem, the existence of positive solutions is established. Moreover, iterative sequences are constructed to approximate the unique positive solution of the problem. Finally, three examples are presented to illustrate the main results.
subject: Articles
  topic: section
subject: p-Laplacian operator
  topic: keywords
subject: tempered fractional derivative
  topic: keywords
subject: fractional differential equation
  topic: keywords
subject: Krasnosel’skii fixed point theorem
  topic: keywords
subject: fixed point theorems for a sum operator
  topic: keywords
creator: Jiqiang Jiang
creator: Minghui Liu
creator: Lishan Liu
creator: Yonghong Wu
rights: Copyright (c) 2026 Jiqiang Jiang | Minghui Liu | Lishan Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
date: 2026-04-28
publication date: 2026-04-28
starting page: 1
ending page: 26
doi: 10.15388/namc.2026.31.46563

Existence and approximate controllability results for time-fractional stochastic Navier–Stokes equations
type: item
description: This paper deals with time-fractional stochastic Navier–Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and approximate controllability of a unique mild solution to time-fractional stochastic Navier–Stokes equations. Using a fixed point technique, we first demonstrate the existence and uniqueness of a mild solution to the equation under consideration. We then establish approximate controllability results by using the concepts of fractional calculus, semigroup theory, functional analysis, and stochastic analysis.
subject: Articles
  topic: section
subject: approximate controllability
  topic: keywords
subject: time-fractional Navier–Stokes equations
  topic: keywords
subject: stochastic analysis
  topic: keywords
subject: semigroup theory
  topic: keywords
subject: fixed point technique
  topic: keywords
creator: Renu Chaudhary
creator: Simeon Reich
creator: Juan. J. Nieto
rights: Copyright (c) 2026 Renu Chaudhary | Simeon Reich | Juan. J. Nieto https://creativecommons.org/licenses/by/4.0
date: 2026-04-21
publication date: 2026-04-21
starting page: 674
ending page: 698
doi: 10.15388/namc.2026.31.46453

Controllability and Ulam–Hyers stability analysis of conformable fractional differential systems with time delays and impulsive effects
type: item
description: We investigate the controllability and Ulam–Hyers stability of a class of conformable fractional differential systems with time delays and impulsive effects. Specifically, we analyze the movement rules before and after the impulse, utilizing both the Banach and Schauder fixed point theorem to derive controllability. Furthermore, we employ nonlinear functional analysis methods to study Ulam–Hyers stability. To demonstrate the applicability and feasibility of our main conclusions, an illustrative example is provided.
subject: Articles
  topic: section
subject: conformable fractional derivative
  topic: keywords
subject: impulse
  topic: keywords
subject: delay
  topic: keywords
subject: controllability
  topic: keywords
subject: Ulam–Hyers stability
  topic: keywords
creator: Luchao Zhang
creator: Xiping Liu
creator: Mei Jia
creator: Zhensheng Yu
creator: Changxiang He
rights: Copyright (c) 2026 Luchao Zhang | Xiping Liu | Mei Jia | Zhensheng Yu | Changxiang He https://creativecommons.org/licenses/by/4.0
date: 2026-04-20
publication date: 2026-04-20
starting page: 651
ending page: 673
doi: 10.15388/namc.2026.31.46446

Existence, uniqueness and averaging principle for fractional Dirichlet boundary value problems driven by Rosenblatt process and Lévy jumps
type: item
description: We address the existence, uniqueness, and averaging principle for Caputo–Hadamard fractional dynamic systems with Dirichlet boundary conditions driven by Rosenblatt process and pure Lévy jumps. First, Lemma 4 establishes the equivalent integral equation representation of our system. Using this foundation, existence and uniqueness are proved by Banach's contraction principle under stochastic calculus, Lipschitz and finite energy conditions. Subsequently, under appropriate averaging assumptions, the system is averaged out with time scale ϵ. Mean-square convergence between original solution and its counterpart is verified by employing tools such as Wiener–Itô double integral, Cauchy–Schwarz, Doob's martingale, and Gronwall–Bellman inequalities. Eventually, computational example with numerical simulations is provided to support the theoretical results.
subject: Articles
  topic: section
subject: Caputo–Hadamard derivative
  topic: keywords
subject: stochastic differential equation
  topic: keywords
subject: averaging principle
  topic: keywords
subject: Lévy jumps
  topic: keywords
subject: Rosenblatt process
  topic: keywords
creator: Jalisraj Arokiyanathan
creator: Ramalingam Udhayakumar
rights: Copyright (c) 2026 Jalisraj Arokiyanathan | Ramalingam Udhayakumar https://creativecommons.org/licenses/by/4.0
date: 2026-04-13
publication date: 2026-04-13
starting page: 627
ending page: 650
doi: 10.15388/namc.2026.31.46362

Fixed-time distributed formation control for nonlinear heterogeneous multiagent systems subject to input nonlinearities and actuator faults
type: item
description: This work focuses on distributed practical fixed-time formation (PFTF) control for heterogeneous multiagent systems (MASs) with inherent nonlinear dynamics, coupled input nonlinearities, and potential actuator faults. Conventional backstepping methods face the challenge of “differential explosion”. To resolve this issue, we propose an innovative command filtering strategy with fixed-time convergence properties, integrated with a compensating mechanism that also ensures fixed-time suppression of filtering errors. Leveraging the synergy of fixed-time control theory, backstepping recursion, and neural networks function approximation, a distributed PFTF control protocol is developed. The designed scheme ensures that the MASs attain the predefined formation configuration within a fixed time, while driving all errors converge to a small residual set. Numerical simulations validate the effectiveness and performance of the proposed approach.
subject: Articles
  topic: section
subject: multiagent systems (MASs)
  topic: keywords
subject: formation control
  topic: keywords
subject: fixed time
  topic: keywords
subject: input nonlinearity and actuator faults
  topic: keywords
subject: command filtered backstepping
  topic: keywords
creator: Jianmin Jiao
creator: Junmin Li
creator: Chao He
creator: Rui Zhang
rights: Copyright (c) 2026 Jianmin Jiao | Junmin Li | Chao He | Rui Zhang https://creativecommons.org/licenses/by/4.0
date: 2026-04-02
publication date: 2026-04-02
starting page: 601
ending page: 626
doi: 10.15388/namc.2026.31.46178

Adaptive fixed-time control with prescribed performance for nonlinear networked control systems under deception attacks
type: item
description: This paper presents a novel fixed-time adaptive control scheme with prescribed performance for nonlinear networked control systems (NCSs) under deception attacks. The Nussbaum function is first employed to tackle the challenge of unknown attack weights and their signs. A hybrid approach integrating a fixed-time performance function with a nonlinear shifting function is used to mitigate the influence of initial conditions on tracking errors. Furthermore, a sufficient condition is derived to guarantee the practical fixed-time stability of NCSs, even in the face of deception attacks. Finally, the effectiveness of the proposed methodology is demonstrated through a mass-spring-damper system simulation.
subject: Articles
  topic: section
subject: deception attacks
  topic: keywords
subject: fixed-time control
  topic: keywords
subject: networked control systems
  topic: keywords
subject: prescribed performance control
  topic: keywords
creator: Linfang Shao
creator: Weiwei Sun
creator: Lusong Ding
rights: Copyright (c) 2026 Linfang Shao | Weiwei Sun | Lusong Ding https://creativecommons.org/licenses/by/4.0
date: 2026-03-24
publication date: 2026-03-24
starting page: 585
ending page: 600
doi: 10.15388/namc.2026.31.46123

Synchronization of quaternion-valued BAM neural networks with time-varying delays
type: item
description: This paper studies the global asymptotic synchronization (GAS) and global exponential synchronization (GES) problems of a class of quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with time-varying delays. Based on the matrix measure approach and Halanay inequality, sufficient conditions for GAS of unbounded time-varying delay system and GES of bounded time-varying delay system were established. Different from existing methods, this approach does not require the construction of Lyapunov functions and obtains the criteria for system synchronization expressed in terms of norms and measures. Finally, the validity of the proposed theoretical results and the feasibility of the control strategy are verified through numerical simulations.
subject: Articles
  topic: section
subject: GAS
  topic: keywords
subject: GES
  topic: keywords
subject: QVBAMNNs
  topic: keywords
subject: matrix measure approach
  topic: keywords
subject: time-varying delays
  topic: keywords
creator: Lu Li
creator: Zhengwen Tu
creator: Tao Peng
creator: Bing Chen
creator: Jiang Xiong
creator: Liangwei Wang
rights: Copyright (c) 2026 Lu Li | Zhengwen Tu | Tao Peng | Bing Chen | Jiang Xiong | Liangwei Wang https://creativecommons.org/licenses/by/4.0
date: 2026-03-20
publication date: 2026-03-20
starting page: 562
ending page: 584
doi: 10.15388/namc.2026.31.46073

Evaluation of domain-specific convolutional neural network layers for galaxy classification tasks
type: item
description: Due to increasing amount of data, galaxy image classification is being automated using machine learning, with the most common approach being convolutional neural networks (CNNs). Using domain-specific observations about galaxy morphology, we propose two CNN layers – Focal and Wave. The Focal layer highlights information in the center, while the Wave layer is designed to highlight spiral arms. A comprehensive evaluation of layers is performed using datasets of 4 and 11 (not yet deeply studied) galaxy types, with and without augmentations. With no augmentations, our models outperform best results of models used in other studies with Wilcoxon signed-rank test's p-value of pF1 = 0.002 for both 4 and 11 classes in terms of F1 score (used to better evaluate performance due to inherent class imbalance). Moreover, our layers help reduce overfitting and reliance on augmentation combinations, as our models, despite benefiting less from augmentations, still achieve results comparable to other augmented models. Additionally, our models tuned for 4-class data perform equally well on 11-class data, and vice versa. Finally, an ensemble of our models trained without augmentations achieves comparable results to our augmented models.
subject: Articles
  topic: section
subject: domain-specific layers
  topic: keywords
subject: galaxy morphology classification
  topic: keywords
subject: Galaxy Zoo
  topic: keywords
subject: model tuning
  topic: keywords
subject: convolutional neural networks
  topic: keywords
creator: Tomas Mūžas
creator: Andrius Vytautas Misiukas Misiūnas
creator: Tadas Meškauskas
rights: Copyright (c) 2026 Tomas Mūžas | Andrius Vytautas Misiukas Misiūnas | Tadas Meškauskas https://creativecommons.org/licenses/by/4.0
date: 2026-03-12
publication date: 2026-03-12
starting page: 544
ending page: 561
doi: 10.15388/namc.2026.31.45923

Adaptive synchronization of quaternion-valued inertial neural networks with uncertain parameters and a flexible time delay
type: item
description: In this paper, a direct method is presented for analyzing the adaptive synchronization of quaternion-valued inertial neural networks (QVINNs) with uncertain parameters and time delay. By this method, the forms of time delays and the Lyapunov function in this paper are flexible, and in stability analysis, the requirement for negative definiteness of Lyapunov functions will be weakened. In addition, a more generalized adaptive synchronization controller has been proposed for QVINNs, which no longer requires multiple calculations of the control gain. Since most of the previous adaptive control methods did not impose requirements on the convergence speed of the QVINNs, a class of improved adaptive controllers is designed to address the slow synchronization speed of QVINNs. Finally, numerical simulations are conducted to validate the synchronization conditions.
subject: Articles
  topic: section
subject: quaternion
  topic: keywords
subject: adaptive synchronization
  topic: keywords
subject: non-separation approach
  topic: keywords
subject: delayed inertial neural networks
  topic: keywords
creator: Xufan Yin
creator: Tao Peng
creator: Jiang Xiong
creator: Zhengwen Tu
creator: Zuxiong Li
creator: Liangwei Wang
rights: Copyright (c) 2026 Xufan Yin | Tao Peng | Jiang Xiong | Zhengwen Tu | Zuxiong Li | Liangwei Wang https://creativecommons.org/licenses/by/4.0
date: 2026-03-02
publication date: 2026-03-02
starting page: 519
ending page: 543
doi: 10.15388/namc.2026.31.45744

Exponential synchronization of quaternion-valued switching neural networks with mixed delays
type: item
description: This paper investigates the exponential synchronization problem for a class of quaternion-valued switching neural networks (QVSNNs) with mixed time delays and sampled-data control. By using a Lyapunov function method involving sampling instants, sufficient conditions for the synchronization of the considered neural networks (NNs) are obtained in the form of linear matrix inequalities (LMIs). It is worth emphasizing that this paper reduces the conservativeness of stability criteria by combining the free-weight matrix method with discrete sampling points; moreover, the derived criteria are valid for both quaternion-valued and nonasynchronous switching NNs. Finally, the feasibility of the proposed approach is verified by two numerical examples.
subject: Articles
  topic: section
subject: quaternion-valued switching neural networks
  topic: keywords
subject: mixed delay
  topic: keywords
subject: LMIs
  topic: keywords
subject: sampled-data control
  topic: keywords
creator: Wei Tan
creator: Yongxiang Zhao
creator: Tao Peng
creator: Zhengwen Tu
creator: Yuan Dong
rights: Copyright (c) 2026 Wei Tan | Yongxiang Zhao | Tao Peng | Zhengwen Tu | Yuan Dong https://creativecommons.org/licenses/by/4.0
date: 2026-03-02
publication date: 2026-03-02
starting page: 496
ending page: 518
doi: 10.15388/namc.2026.31.45743

Prescribed-time leader-following scaled consensus for nonlinear multiagent systems
type: item
description: In this paper, the leader-following (L-F) scaled consensus (SC) for first-order multiagent systems (MASs) is considered within a prescribed time (PT). First, a distributed control protocol is proposed by incorporating a time-varying gain function and scaled factors. This protocol is designed to drive the states of the leader and followers to a predefined scaled relationship within the PT. It is worth noting that, by appropriately selecting the scaled factor, the protocol can also achieve complete consensus, bipartite consensus, or cluster consensus among the agents. To further enhance the control performance and reduce communication frequency, an improved control protocol is proposed by incorporating an event-triggered mechanism in which the event-triggering function is constructed using time-varying variables. Moreover, based on the PT stability theory, sufficient conditions are derived to ensure that SC is achieved within the PT. Finally, the effectiveness of the proposed control protocol is verified through two numerical simulation examples.
subject: Articles
  topic: section
subject: prescribed time
  topic: keywords
subject: scaled consensus
  topic: keywords
subject: nonlinear MASs
  topic: keywords
subject: event-triggered protocol
  topic: keywords
subject: time-varying scaling function
  topic: keywords
creator: Chongjiao Qian
creator: Zhiyong Yu
creator: Haijun Jiang
rights: Copyright (c) 2026 Chongjiao Qian | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
date: 2026-03-02
publication date: 2026-03-02
starting page: 477
ending page: 495
doi: 10.15388/namc.2026.31.45742

An open-source parallel algorithm of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems
type: item
description: Contemporary engineering and scientific problems often involve computationally intensive optimization tasks. This paper proposes a parallel version of the hybrid algorithm of the previously proposed Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems. The Bayesian-based hybrid algorithm has been complemented with multi-process data exchange using Open MPI to obtain a scalable parallel application. Each parallel process executes the Bayesian-based hybrid algorithm, and at the end, the Pareto optimal solutions of each process are merged into an aggregated set of Pareto optimal solutions. The master-slave pattern was used to parallelize the computations, where slave processes execute optimization algorithm and then send the obtained Pareto optimal solutions to the master process, which, in turn, also executes optimization algorithm and merges the Pareto optimal solutions of all processes. The developed parallel algorithm was tested under the same conditions previously used for testing other Bayesian algorithms to enable comparison of performance. Finally, the proposed parallel algorithm was published on the GitHub developer platform for code sharing.
subject: Articles
  topic: section
subject: global optimization
  topic: keywords
subject: Bayesian algorithm
  topic: keywords
subject: Hooke–Jeeves algorithm
  topic: keywords
subject: open-source parallel algorithm
  topic: keywords
creator: Linas Litvinas
rights: Copyright (c) 2026 Linas Litvinas https://creativecommons.org/licenses/by/4.0
date: 2026-02-25
publication date: 2026-02-25
starting page: 463
ending page: 476
doi: 10.15388/namc.2026.31.45618

Entropy generation for MHD pulsating stratified liquid flow between two permeable beds
type: item
description: In natural systems such as lakes, reservoirs, and the upper ocean layers, temperature-induced stratified fluid flows are frequently observed. Numerous studies have explored key aspects of these flows, including stability, mixing, and thermal transport. However, the heat transfer characteristics of stratified fluid flow between permeable beds remain unexplored. This study aims to address this gap by performing an entropy generation analysis of pulsating stratified fluid flow between two permeable beds, with key applications in geothermal energy extraction, environmental modelling, and biomedical engineering. Liquid is injected through the lower bed and extracted from the upper bed at an equal velocity. The governing flow equations are solved numerically using the fourth-order Runge–Kutta (RK-4) method in combination with the shooting method in Mathematica. Graphical results are presented to illustrate the influence of key parameters on velocity, temperature, Nusselt number, entropy generation, Bejan number, mass flux, and stress distribution. Our results indicated that a rise in the Reynolds number, pressure gradient, and stratification parameter boosts the fluid velocity, while a higher slip parameter tends to reduce it. The temperature distribution declines with the rise of magnetic field and Reynolds number. In contrast, it intensifies with elevated Brinkman number, pressure gradient, and stratification parameter.
subject: Articles
  topic: section
subject: stratified fluid
  topic: keywords
subject: permeable bed
  topic: keywords
subject: Bejan number
  topic: keywords
subject: Nusselt number
  topic: keywords
creator: Madhurya Vangalapudi
creator: Suripeddi Srinivas
rights: Copyright (c) 2026 Madhurya Vangalapudi | Suripeddi Srinivas https://creativecommons.org/licenses/by/4.0
date: 2026-02-16
publication date: 2026-02-16
starting page: 443
ending page: 462
doi: 10.15388/namc.2026.31.45383

Exact solutions of stochastic generalized long–short wave resonance equations with cubic–quintic nonlinearity via the new sub-ODE method
type: item
description: We study a stochastic generalized long–short wave resonance system with cubic–quintic nonlinearities, perturbation terms, and multiplicative white noise in the Itô sense. Using a traveling-wave reduction combined with the newly proposed sub-ODE method, we construct explicit families of solitary-wave and elliptic-function solutions, including elevation, depression, and singular branches. The analysis reveals how stochastic effects shrink the existence domains of these solutions, while a Hamiltonian linearization provides Vakhitov–Kolokolov- and Grillakis–Shatah–Strauss-type stability criteria. The results enrich nonlinear wave theory and offer insights relevant to solitary-wave applications in fiber optics and related technologies.
subject: Articles
  topic: section
subject: embedded solitons
  topic: keywords
subject: long–short wave
  topic: keywords
subject: new sub-ODE method
  topic: keywords
subject: cubic–quintic nonlinearity
  topic: keywords
subject: multiplicative white noise
  topic: keywords
creator: Elsayed M.E. Zayed
creator: Basel M.M. Saad
creator: Mir Sajjad Hashemi
creator: Muhammad Amin S. Murad
creator: Ahmed H. Arnous
creator: Mustafa Bayram
rights: Copyright (c) 2026 Elsayed M.E. Zayed | Basel M.M. Saad | Mir Sajjad Hashemi | Muhammad Amin S. Murad | Ahmed H. Arnous | Mustafa Bayram https://creativecommons.org/licenses/by/4.0
date: 2026-02-13
publication date: 2026-02-13
starting page: 421
ending page: 442
doi: 10.15388/namc.2026.31.45367

Improved fixed-time consensus of delayed nonlinear leader–follower multi-agent systems
type: item
description: This article aims to study the problem of fixed-time consensus for nonlinear leader–follower multi-agent systems (MASs) with time delay. Firstly, a new fixed-time stability lemma is derived, where the condition of inequality contains a time-delayed term. Furthermore, a more precise estimated value of settling time (ST) including delayed parameter is obtained, which is different from those existing fixed-time stability lemmas. Thereby, it provides some options for designers in many practical scenarios when considering the delayed systems. Secondly, for the purpose of explaining its applicability, fixed-time consensus of leader–follower nonlinear MASs is investigated by designing a nonlinear control protocol including constant time delay. The designed protocol not only guarantees fixed-time consensus but also effectively improves the convergence rate. With the new proposed lemma, a novel consensus criterion is designed. This is the first time to obtain the time-delayed dependent fixed-time stability criterion for MASs. Finally, the validity and superiority of the established theoretical results are confirmed by one numerical simulation.
subject: Articles
  topic: section
subject: multi-agent systems
  topic: keywords
subject: fixed-time consensus
  topic: keywords
subject: fixed-time stability
  topic: keywords
subject: time-delayed systems
  topic: keywords
creator: Mingqiang Meng
creator: Qintao Gan
creator: Ruihong Li
creator: Luke Li
creator: Qiaokun Kang
creator: Hao Chang
rights: Copyright (c) 2026 Mingqiang Meng | Qintao Gan | Ruihong Li | Luke Li | Qiaokun Kang | Hao Chang https://creativecommons.org/licenses/by/4.0
date: 2026-02-11
publication date: 2026-02-11
starting page: 398
ending page: 420
doi: 10.15388/namc.2026.31.45328

Finite-time matrix projective synchronization of fractional-order memristor-based delayed neural networks with parameter uncertainty
type: item
description: This research examines the phenomenon of finite-time matrix projective synchronization (FTMPS) in the context of two distinct fractional-order memristor-based delayed neural networks (FOMDNNs). For the FOMDNNs with indeterminate parameters, some suitable controllers are structured, and sufficient conditions for implementing the FTMPS are demonstrated through some inequality techniques and relevant lemmas pertaining to fractional calculus. The synchronization issues under two different norm cases are fully considered. Subsequently, two numerical examples of the FTMPS are revealed and the discrepancies in their synchronization gradually tend to zero, which shows the validity and accuracy of the obtained synchronization results.
subject: Articles
  topic: section
subject: Caputo derivative
  topic: keywords
subject: finite-time synchronization
  topic: keywords
subject: parameter uncertainty
  topic: keywords
subject: fractional-order memristive-based delayed neural networks
  topic: keywords
creator: Shangbin Xu
creator: Bo Hu
creator: Hai Zhang
creator: Xinbin Chen
creator: Jinde Cao
rights: Copyright (c) 2026 Shangbin Xu | Bo Hu | Hai Zhang | Xinbin Chen | Jinde Cao https://creativecommons.org/licenses/by/4.0
date: 2026-02-07
publication date: 2026-02-07
starting page: 376
ending page: 397
doi: 10.15388/namc.2026.31.45269

Stability and stabilization for positive switched delay systems under mode-dependent interval dwell time
type: item
description: This paper explores the issues of exponential stability and positive stabilization of positive switched systems with time-varying delays. Using the Lyapunov–Razumikhin approach, we derive exponential stability criteria for positive switched delay systems (PSDSs) across various switching behaviors, including nondecreasing and decreasing switching patterns. Following this, we delve into the design of state feedback control to achieve positive stabilization of these systems, leveraging the established stability conditions. The paper culminates with numerical examples that confirm the validity of our theoretical findings.
subject: Articles
  topic: section
subject: positive switched systems
  topic: keywords
subject: exponential stability
  topic: keywords
subject: positive stabilization
  topic: keywords
subject: time-varying delay
  topic: keywords
subject: mode-dependent interval dwell time
  topic: keywords
creator: Xiukun Zhang
creator: Yuangong Sun
rights: Copyright (c) 2026 Xiukun Zhang | Yuangong Sun https://creativecommons.org/licenses/by/4.0
date: 2026-01-25
publication date: 2026-01-25
starting page: 351
ending page: 375
doi: 10.15388/namc.2026.31.45028

Adaptive event-triggered output-feedback stabilization for nonlinear systems with function control coefficients
type: item
description: This article presents an adaptive event-triggered control scheme for global stabilization of uncertain nonlinear systems with function control coefficients, input matching uncertainty, and unknown polynomial-function rates. A single dynamic gain observer is designed to handle these complexities, replacing the traditional dual-gain approach. An extended state observer asymptotically estimates the input matching uncertainty. An adaptive output-feedback controller, based on a time-varying threshold event-triggering mechanism, ensures closed-loop system stabilization and prevents Zeno behavior. Simulation results validate the proposed strategy
subject: Articles
  topic: section
subject: uncertain nonlinear systems
  topic: keywords
subject: function control coefficients
  topic: keywords
subject: input matching uncertainty
  topic: keywords
subject: event-triggered output feedback
  topic: keywords
creator: Yu Zhang
creator: Shaoli Jin
creator: Hui Li
creator: Yue Pan
rights: Copyright (c) 2026 Yu Zhang | Shaoli Jin | Hui Li | Yue Pan https://creativecommons.org/licenses/by/4.0
date: 2026-01-22
publication date: 2026-01-22
starting page: 330
ending page: 350
doi: 10.15388/namc.2026.31.44986

Observer-based distributed optimization for linear multiagent systems with external disturbances
type: item
description: This paper addresses the distributed optimization problem in linear multiagent systems (MASs) under external disturbances. Firstly, an observation system is designed by utilizing the output values of agents, which can eliminate external disturbances of system. Secondly, an event-triggered control algorithm is proposed through the gradient information of local cost functions, and its convergence is rigorously established using the Lyapunov stability and looped functional theory. This novel event-triggered protocol incorporates dwell time within the threshold function, effectively eliminating Zeno behavior. By leveraging the looped functional technique, more relaxed conditions are derived for solving the distributed optimization problem. Finally, the validity and feasibility of the proposed protocol are substantiated through numerical simulation.
subject: Articles
  topic: section
subject: external disturbances
  topic: keywords
subject: multiagent system
  topic: keywords
subject: distributed optimization
  topic: keywords
subject: looped functional method
  topic: keywords
creator: Xuening Xu
creator: Zhiyong Yu
creator: Haijun Jiang
rights: Copyright (c) 2026 Xuening Xu | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
date: 2026-01-07
publication date: 2026-01-07
starting page: 311
ending page: 329
doi: 10.15388/namc.2026.31.44762

Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
type: item
description: We investigate a triple system of fractional Sturm–Liouville–Langevin equations with cyclic antiperiodic boundary conditions. The fixed point theorem serves as a tool to establish the existence and uniqueness criteria for solutions. By applying the Banach contraction principle, we also obtain the Ulam–Hyers stability of the proposed system. Finally, examples are provided to illustrate main results.
subject: Articles
  topic: section
subject: fractional Sturm–Liouville–Langevin equation
  topic: keywords
subject: triple system
  topic: keywords
subject: existence and uniqueness
  topic: keywords
subject: Ulam-types stability
  topic: keywords
creator: Gang Chen
creator: Zhanbing Bai
creator: Wei Zhang
rights: Copyright (c) 2026 Gang Chen | Zhanbing Bai | Wei Zhang https://creativecommons.org/licenses/by/4.0
date: 2026-01-05
publication date: 2026-01-05
starting page: 285
ending page: 310
doi: 10.15388/namc.2026.31.44744

Energetic formulation of the subgroup commutativity degree
type: item
description: Finite groups in which every pair of subgroups (H, K) satisfies H K = K H have been classified by Iwasawa, but only in the last decade it was introduced the notion of subgroup commutativity degree sd(G) of groups G. From restrictions of numerical nature on sd(G) one usually derives structural conditions on G; in fact, among groups G with sd(G) = 1, one finds those originally studied by Iwasawa. Here we offer a new perspective of study for sd(G); we use a recently introduced graph, which is called nonpermutability graph of subgroups ΓL(G) of G, in order to restrict sd(G) via the notion of energy of ΓL(G) and by means of methods of spectral graph theory. In particular, we find new criteria of nilpotence for G along with new bounds for sd(G).
subject: Articles
  topic: section
subject: spectral graph theory
  topic: keywords
subject: energy of a graph
  topic: keywords
subject: subgroup commutativity degree
  topic: keywords
subject: nonpermutability graph of subgroups
  topic: keywords
subject: adjacency matrix
  topic: keywords
creator: Seid Kassaw Muhie
creator: Daniele Ettore Otera
creator: Francesco G. Russo
rights: Copyright (c) 2026 Seid Kassaw Muhie | Daniele Ettore Otera | Francesco G. Russo https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 212
ending page: 236
doi: 10.15388/namc.2026.31.44490

Nonparametric changed segment detection in functional data
type: item
description: We address the epidemic change point detection problem without parametric assumptions. We propose statistics based on Cramér–von Mises-type statistic and reproducing kernel Hilbert space that iterate through all interval subsets, rescaling them to remain sensitive to both short and long epidemics. We prove limit theorems and provide quantiles for both statistics under the different parametrizations. The simulations show consistent power across a wide range of scenarios, and an application to electricity balancing prices consistently detects a market disturbance.
subject: Articles
  topic: section
subject: epidemic change
  topic: keywords
subject: reproducing kernel Hilbert space
  topic: keywords
subject: Cramér–von Mises-type statistic
  topic: keywords
creator: Karolis Bartkus
creator: Alfredas Račkauskas
rights: Copyright (c) 2026 Karolis Bartkus | Alfredas Račkauskas https://creativecommons.org/licenses/by/4.0
date: 2026-01-01
publication date: 2026-01-01
starting page: 194
ending page: 211
doi: 10.15388/namc.2026.31.44489