Nonlinear Analysis: Modelling and Control
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.
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Evaluation of domain-specific convolutional neural network layers for galaxy classification tasks
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.
Copyright (c) 2026 Tomas Mūžas | Andrius Vytautas Misiukas Misiūnas | Tadas Meškauskas https://creativecommons.org/licenses/by/4.0
Adaptive synchronization of quaternion-valued inertial neural networks with uncertain parameters and a flexible time delay
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.
Copyright (c) 2026 Xufan Yin | Tao Peng | Jiang Xiong | Zhengwen Tu | Zuxiong Li | Liangwei Wang https://creativecommons.org/licenses/by/4.0
Exponential synchronization of quaternion-valued switching neural networks with mixed delays
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.
quaternion-valued switching neural networks
Copyright (c) 2026 Wei Tan | Yongxiang Zhao | Tao Peng | Zhengwen Tu | Yuan Dong https://creativecommons.org/licenses/by/4.0
Prescribed-time leader-following scaled consensus for nonlinear multiagent systems
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.
Copyright (c) 2026 Chongjiao Qian | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
An open-source parallel algorithm of Bayesian-based global search with Hooke–Jeeves local refinement for multi-objective optimization problems
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.
Copyright (c) 2026 Linas Litvinas https://creativecommons.org/licenses/by/4.0
Entropy generation for MHD pulsating stratified liquid flow between two permeable beds
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.
Copyright (c) 2026 Madhurya Vangalapudi | Suripeddi Srinivas https://creativecommons.org/licenses/by/4.0
Exact solutions of stochastic generalized long–short wave resonance equations with cubic–quintic nonlinearity via the new sub-ODE method
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.
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
Improved fixed-time consensus of delayed nonlinear leader–follower multi-agent systems
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.
Copyright (c) 2026 Mingqiang Meng | Qintao Gan | Ruihong Li | Luke Li | Qiaokun Kang | Hao Chang https://creativecommons.org/licenses/by/4.0
Finite-time matrix projective synchronization of fractional-order memristor-based delayed neural networks with parameter uncertainty
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.
fractional-order memristive-based delayed neural networks
Copyright (c) 2026 Shangbin Xu | Bo Hu | Hai Zhang | Xinbin Chen | Jinde Cao https://creativecommons.org/licenses/by/4.0
Stability and stabilization for positive switched delay systems under mode-dependent interval dwell time
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.
Copyright (c) 2026 Xiukun Zhang | Yuangong Sun https://creativecommons.org/licenses/by/4.0
Adaptive event-triggered output-feedback stabilization for nonlinear systems with function control coefficients
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
Copyright (c) 2026 Yu Zhang | Shaoli Jin | Hui Li | Yue Pan https://creativecommons.org/licenses/by/4.0
Observer-based distributed optimization for linear multiagent systems with external disturbances
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.
Copyright (c) 2026 Xuening Xu | Zhiyong Yu | Haijun Jiang https://creativecommons.org/licenses/by/4.0
Existence and stability results for triple systems of fractional Sturm–Liouville–Langevin equations with cyclic boundary conditions
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.
fractional Sturm–Liouville–Langevin equation
Copyright (c) 2026 Gang Chen | Zhanbing Bai | Wei Zhang https://creativecommons.org/licenses/by/4.0
Energetic formulation of the subgroup commutativity degree
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).
Copyright (c) 2026 Seid Kassaw Muhie | Daniele Ettore Otera | Francesco G. Russo https://creativecommons.org/licenses/by/4.0
Nonparametric changed segment detection in functional data
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.
Copyright (c) 2026 Karolis Bartkus | Alfredas Račkauskas https://creativecommons.org/licenses/by/4.0
Modeling the impact of detritus-based irrigation on agricultural crop production
The excessive use of chemical fertilizers in agricultural farms poses a serious threat to nearby water bodies, such as lakes, ponds, etc., by causing algal blooms in these water bodies and also put agricultural sustainability at risk. This study deals with the use of algae-rich pond water for irrigation, which impacts soil fertility through organic detritus. A nonlinear mathematical model is formulated to analyze the ecological and agronomic impacts of this irrigation approach. The formulation of the model takes into account that the detritus-based pond water used for irrigation initially benefits the crop growth; but once it exceeds a certain threshold, reduces the crop yield. Furthermore, the model demonstrates how nature-based solutions can be strategically integrated into agricultural system to achieve long-term resilience. The study identifies key thresholds and behavioral transitions by detecting a saddle-node, transcritical, and Hopf bifurcations within the proposed mathematical model. To support analytical findings, we conduct numerical simulations that provide a strong evidence of the agricultural ecosystem’s resilience particularly in maintaining the crop yield under the modeled irrigation conditions. These simulations underscore the potential for managing detritus density to optimize crop productivity while minimizing ecological risks. Findings of this study can support the environment-friendly irrigation policies suited to different agroecological regions. Study reveals that detritus-based irrigation promotes crop productivity up to a critical threshold of detritus input, beyond which its effects turn inhibitory. Simultaneously, it suppresses algal blooms, thereby uncovering a natural self-regulating mechanism with significant implications for sustainable irrigation practices and nutrient management policies.
Copyright (c) 2026 Arvind Kumar Misra | Prinsi Shukla https://creativecommons.org/licenses/by/4.0
New strong convergence algorithms for general equilibrium and variational inequality problems and resolvent operators in Banach spaces
In this paper, we introduce two new algorithms for solving variational inequalities in Banach spaces. Our aim is finding a common element of the solution set of variational inequalities (for two inverse-strongly monotone operators) and an equilibrium problem and the set of fixed points of two relatively nonexpansive mappings and a family of resolvent operators. Then the strong convergence of the sequences generated by these algorithms to this element will be proved under suitable conditions. Finally, we provide a numerical example to illustrate our main results.
Copyright (c) 2026 Mostafa Ghadampour | Ebrahim Soori | Ravi P. Agarwal | Donal O’Regan https://creativecommons.org/licenses/by/4.0
Copyright (c) 2026 Artūras Štikonas https://creativecommons.org/licenses/by/4.0
Dynamical investigation of the nonlinear Schrödinger equation with second-order spatiotemporal involvement of the time-conformable operator
The article analyzes the application of the extended hyperbolic function technique to a conformable-operator nonlinear Schrödinger equation, incorporating group velocity dispersion coefficients and second-order spatiotemporal components. The primary objective is establishing a spectrum of solutions directly pertinent to optical fibers. The extracted results, which include bright, singular, straddled, dark-bright, and dark solitons, are obtained by hyperbolic and trigonometric function-type solutions. We exhibit contour plots with two-dimensional and three-dimensional visualizations to emphasize the implication of the proposed conformable-operator nonlinear Schrödinger equation and to depict the diverse novel optical solutions. Additionally, we study the impact of the conformable operator on these solutions, employing graphical analysis to demonstrate its implications. The governing model shows potential applications in transmitting ultra-fast pulses via optical fibers.
nonlinear conformable Schrödinger equation
Copyright (c) 2026 Muhammad Amin S. Murad | Faraidun Kadir Hamasalh | Mujahid Iqbal | Sandeep Malik | Ahmed H. Arnous https://creativecommons.org/licenses/by/4.0
Fundamental contractions in suprametric spaces
In this manuscript, we propose the notion of a strong extended s-suprametric space, a novel extension that outperforms both s-suprametric and extended suprametric spaces. It looks into the aspects of open and closed ball topologies within this structure. It also investigates the concepts of existence and uniqueness using basic contractions viz. Banach and Kannan contractions. Illustrative examples demonstrate how the strong extended s-suprametric space outperforms its extended equivalent. Our examples demonstrate the presence and distinctness of fixed points in this scenario. Furthermore, exploiting these newly launched results, the manuscript investigates the analysis of a boundary value problem, including diffusing chemical material constrained between parallel walls with related concentrations at the boundaries, taking into account supplied raw density and recognized absorbing coefficients. It also applies these insights to a nonlinear boundary value issue involving satellite web coupling in which a thin sheet joins two cylindrical spacecraft. This coupling causes nonlinearity, resulting in a separate boundary value issue influenced by radiation effects within the satellites.
Copyright (c) 2026 Saad Jamhan Aldosari | Haroon Ahmad | Mudasir Younis | Mahpeyker Öztürk | Farwa Asmat https://creativecommons.org/licenses/by/4.0
Monotone iterative sequences for positive solutions of a p-Laplacian Hadamard fractional boundary value problem on an unbounded domain
In this paper, we ensure the existence and uniqueness of positive solutions for a Hadamard fractional boundary value problem with the p-Laplacian operator on an unbounded domain. The problem is formulated as a nonlinear differential equation involving a fractional derivative of order ℓ ∈ (n – 1, n], n ∈ N, along with boundary conditions of the Hadamard fractional integral and derivative. Using the monotone iterative technique, we establish the existence of positive solutions by constructing monotone sequences that approach the solution. An error estimation formula is provided. An example is also discussed to illustrate the main result.
Copyright (c) 2026 Fulya Yoruk Deren | Tugba Senlik Cerdik | Ravi P. Agarwal https://creativecommons.org/licenses/by/4.0
Exact controllability of conformable linear systems with semilinear boundary control
In this manuscript, we investigate the exact controllability of a class of linear systems governed by conformable fractional derivatives of order α in (0; 1] subject to semilinear boundary control in Banach spaces. We first establish the existence of mild solutions to the associated fractional Cauchy problems. We then derive sufficient conditions ensuring the exact controllability of these conformable linear systems under semilinear boundary control actions. An abstract model of an age-structured population dynamics system is provided to illustrate the applicability of the theoretical results.
Copyright (c) 2026 Abdellah Lourini | Mohamed El Azzouzi | Mohamed Laabissi https://creativecommons.org/licenses/by/4.0
Relative controllability of damped fractional differential system with distributed delays and impulses
In this paper, we deal with the relative controllability of linear and nonlinear damped fractional differential system with distributed delays and impulses. The sufficient and necessary conditions for the relative controllability of the linear system under consideration are given by using the controllability Gramian matrix. We also prove a sufficient condition on the nonlinear term to ensure that the above system is relative controllable. Two instances are provided to verify that our theoretical results are accurate.
Copyright (c) 2026 Wangmin An | Danfeng Luo https://creativecommons.org/licenses/by/4.0
An analytical study of the time-fractional extended shallow-water wave equation in (3 + 1)-dimension with two different derivatives and their comparison
In ocean physics, an essential mathematical framework for examining the dynamic behavior of waves is the (3 + 1)-dimensional generalized shallow-water wave equation. This approach is driven by the growing need to incorporate nonlinear and anomalous behaviors in shallow-water wave propagation into more realistic mathematical models. This motivation is a key consideration for improving coastal hazard prediction, mitigating tsunami impacts, optimizing renewable energy extraction, and deepening our understanding of complex coastal processes. In this paper, exact solutions of the fractional generalized shallow-water wave equation are constructed using two alternative methods: the extended modified auxiliary equation mapping method and the F-expansion approach. The extended modified auxiliary equation mapping method yielded nineteen exact solutions across two main sets, while the F-expansion method produced solutions for seventeen different cases. To visualize these, 2D and 3D graphical representations have been generated for several solutions using fractional parameter values α ∈ (0; 1], including sample values such as 0.2, 0.5, 0.7, and 0.78, to illustrate how the order of the derivative affects the soliton profile. The results show that decreasing α leads to broader and smoother soliton structures. Finally, the modulation instability of the governing model is also investigated, confirming that the established results are stable.
the extended modified auxiliary equation mapping method
Copyright (c) 2026 Esra Ünal Yılmaz | Yeçim Sağlam Özkan https://creativecommons.org/licenses/by/4.0
Quantization-based event-triggered control for synchronization of 2-D discrete-time switched master-slave systems in Roesser model
This paper investigates synchronization control for 2-D discrete-time switched master-slave systems modeled by the Roesser framework, which is classic for spatiotemporal dynamics in 2-D systems. A novel quantization-based event-triggered control strategy is proposed to handle complexities from switching dynamics, discrete-time features, and spatial coupling, while considering limited communication resources. By designing a mode-dependent event-triggered strategy and constructing mode-dependent Lyapunov functions for horizontal and vertical dynamics, new sufficient conditions are derived to ensure global exponential synchronization (GES) of the system. The approach relaxes strict stability requirements for individual modes, allowing global stability even with unstable modes. Additionally, the integration of quantization techniques and event-triggered mechanisms significantly reduces data transmission, thereby optimizing network bandwidth usage. Numerical simulations verify the method’s effectiveness.
Copyright (c) 2026 Zhimin Zhou | Lei Shi | Wenbo Liu | Xilong Luo | Shiqi Mo | Jiayin Mou https://creativecommons.org/licenses/by/4.0
Null controllability of Chafee–Infante equation under discrete-time point measurements
Nonlinear system is one of the main research objects in cybernetics, and it is the main theme of cybernetics in the 21st century. Recently, the control of the reaction–diffusion equation has been widely studied, but the nonlinear reaction–diffusion equation has been rarely studied. This paper will take the Chafee–Infante equation as an example, and the null controllability of this equation will be shown. We consider the null controllability for Chafee–Infante equation with point actuations subject to a known constant delay. The point measurements can be sampled in time and transmitted through a communication network with a time-varying delay. We design an observer for the future value of the state in order to compensate the input delay, then we ensure that the estimation error vanishes exponentially with a desired decay rate by using a time-varying observer gain. By constructing Lyapunov–Krasovskii functional and combining linear matrix inequalities (LIMs), we obtain the convergence conditions. We design the boundary controller and the point controller, and we conclude that both controllers can ensure the exponential stability of the closed-loop system with an arbitrary decay rate, which is smaller than that of the observers estimation error. At last, numerical example is given.
Chafee–Infante reaction–diffusion equation
Copyright (c) 2026 Shuai Guo | Yuan Yuan Qin | Guangying Lv | Guang-an Zou https://creativecommons.org/licenses/by/4.0
Trajectory controllability of semilinear dynamic systems on time scales
This paper explores the trajectory controllability of semilinear dynamic systems defined over time scales, which is an important aspect in understanding and manipulating the behavior of such systems across discrete and continuous domains. We address the controllability of these systems under the assumption that the nonlinearities satisfy a Lipschitz-type condition. Our approach involves a detailed analysis of how these conditions impact the ability to steer the system’s state along a desired trajectory within a finite-time horizon. We establish sufficient conditions for trajectory controllability (T-controllability), providing a theoretical framework that extends classical results from differential and difference equations to the broader context of time-scale calculus. To illustrate the practical implications of our theoretical findings, we include several numerical examples that demonstrate the application of our results to specific semilinear dynamic systems, highlighting the versatility and effectiveness of our approach.
Copyright (c) 2026 Sakthivel Shivasivapriyaa | Shanmugasundaram Karthikeyan | Venkatesan Govindaraj | Dimplekumar Chalishajar https://creativecommons.org/licenses/by/4.0
On the h-manifolds for impulsive conformable neural networks with reaction–diffusion terms
In this paper, we consider a new class of conformable impulsive reaction–diffusion neural networks. The stable behavior of h-manifolds with respect to the model is investigated, and sufficient conditions are proposed by constructing suitable Lyapunov-like functions. Our results are new and contribute to the development of the theory of impulsive conformable models. Examples are also presented to illustrate the proposed criteria.
Copyright (c) 2025 Anatoliy Martynyuk | Gani Stamov | Ivanka Stamova https://creativecommons.org/licenses/by/4.0
Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
This article explores the novel approach to addressing the intra/inter-layer synchronization challenges in stochastic multi-layer networks (SMLNs). First, considering the influence of time delay in control, an event-triggered delayed impulsive control (ETDIC) strategy is developed, where the impulsive instant is determined by the predesigned event-triggered mechanism. Moreover, by introducing piecewise auxiliary functions, it effectively excludes Zeno behavior within the ETDIC framework. The study then derives sufficient conditions for ensuring intra- and inter-layer; synchronization, leveraging the Lyapunov method and rigorous mathematical analysis. Finally, theoretical results are validated through numerical simulations.
event-triggered delayed impulsive control
Copyright (c) 2025 Hengyu Liu | Jiarong Li | Haijun Jiang | Jinling Wang | Cheng Hu https://creativecommons.org/licenses/by/4.0
An advanced visualization of self-organizing maps by determining data clusters
This paper proposes a novel approach to improve the visualization capabilities of self-organizing maps and facilitate the identification of the resulting clusters. Unlike other clustering algorithms, self-organizing maps lack the feature to select a predefined number of clusters, and the boundaries of the clusters are not explicitly represented on the self-organizing maps. The main advantage of our proposed approach is that the option for selecting the desired number of clusters has been implemented. The experimental investigation was performed using four datasets with different characteristics. The improved visualization leverages various similarity distances to assess their impact on performance. The effectiveness of the novel approach to clustering results has been compared with those of the well-known k-means and hierarchical clustering methods, which allow for the selection of the desired number of clusters. Additionally, the visualization results, obtained by the proposed approach, were compared with those produced using the Orange Data Mining tool, where the u-matrix is applied to visualize a self-organizing map. The advantage of our approach compared to the u-matrix visualization has been highlighted in this paper. The performance of clustering algorithms has been measured by calculating the ratio of data items correctly assigned to clusters in the case when the clusters are predefined in the analyzed dataset. The results obtained showed that the most effective similarity distances are the cosine and correlation distances, which help to detect the correctly predefined clusters in the visualization of self-organizing maps.
Copyright (c) 2025 Pavel Stefanovič | Olga Kurasova https://creativecommons.org/licenses/by/4.0