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: On the h-manifolds for impulsive conformable neural networks with reaction–diffusion terms
items: Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
items: An advanced visualization of self-organizing maps by determining data clusters
items: Boundary value problems for third-order differential equations involving singular Phi-Laplacian operators
items: Spatiotemporal dynamics of a modified Leslie–Gower predator–prey model: Effects of diffusion and taxis-driven movements on pattern formation
items: Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices
items: Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation
items: Exploring fixed points via admissibility criteria for fuzzy theta f-weak contractions
items: Existence of nontrivial solutions for a class of 2n-order ODE
items: A new dynamic model for simultaneous saccharification and fermentation process of rice wine
items: Efficient computation of blood velocity in the left atrial appendage: A practical perspective
items: Background risk model in presence of heavy tails under dependence
items: Stability analysis of leptospirosis compartmental model with impact of contaminated environment
items: Finite-time synchronization and quasi-synchronization of fractional-order fuzzy BAM neural networks with time delays
items: On a novel semigroup of enriched Chatterjea-type mappings in Banach spaces with a numerical experiment
items: A revisit to tail risk measures in the presence of bivariate regularly varying tailed insurance and financial risks
items: Numerical algorithms to solve one inverse problem for Navier–Stokes equations
items: Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions
items: A mathematical model for degradation of forest area by industrialization causing migration of wildlife species
items: Analysis and exact solutions for reaction–diffusion predator–prey system with prey-taxis by phi6 method
items: M-matrices and one-dimensional discrete Sturm–Liouville problems with nonlocal boundary conditions
items: A new class of integral-multipoint boundary value problems for nonlinear Hadamard fractional differential equations on a semiinfinite domain
items: A class of nonlinear double-phase Dirichlet fractional differential equations
items: Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order complex-valued neural networks with time delays and discontinuous activations
items: Controllability of stochastic impulsive integro-differential systems involving nonlocal conditions and conformable derivatives
items: Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws
items: Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach
items: Finite-time stability of discrete fractional uncertain recurrent neural networks
items: Message spreading modeling from the perspective of social psychology, differential equation dynamics, and deep learning technique
items: On well-posedness and decay of Active model B

On the h-manifolds for impulsive conformable neural networks with reaction–diffusion terms
type: item
description: 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.
subject: Articles
  topic: section
subject: conformable derivatives
  topic: keywords
subject: neural networks
  topic: keywords
subject: reaction–diffusion terms
  topic: keywords
subject: practical stability
  topic: keywords
subject: impulses
  topic: keywords
subject: h-manifolds
  topic: keywords
creator: Anatoliy Martynyuk
creator: Gani Stamov
creator: Ivanka Stamova
rights: Copyright (c) 2025 Anatoliy Martynyuk | Gani Stamov | Ivanka Stamova https://creativecommons.org/licenses/by/4.0
date: 2025-10-23
publication date: 2025-10-23
starting page: 1211
ending page: 1231
doi: 10.15388/namc.2025.30.43844

Synchronization analysis for stochastic multi-layer networks: Event-based impulsive control with predefined impulsive intervals
type: item
description: 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.
subject: Articles
  topic: section
subject: stochastic multi-layer networks
  topic: keywords
subject: intra-layer synchronization
  topic: keywords
subject: inter-layer synchronization
  topic: keywords
subject: event-triggered delayed impulsive control
  topic: keywords
creator: Hengyu Liu
creator: Jiarong Li
creator: Haijun Jiang
creator: Jinling Wang
creator: Cheng Hu
rights: Copyright (c) 2025 Hengyu Liu | Jiarong Li | Haijun Jiang | Jinling Wang | Cheng Hu https://creativecommons.org/licenses/by/4.0
date: 2025-10-20
publication date: 2025-10-20
starting page: 1186
ending page: 1210
doi: 10.15388/namc.2025.30.43839

An advanced visualization of self-organizing maps by determining data clusters
type: item
description: 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.
subject: Articles
  topic: section
subject: self-organizing maps
  topic: keywords
subject: u-matrix
  topic: keywords
subject: similarity distances
  topic: keywords
subject: visualization
  topic: keywords
subject: data clustering
  topic: keywords
subject: number of clusters
  topic: keywords
creator: Pavel Stefanovič
creator: Olga Kurasova
rights: Copyright (c) 2025 Pavel Stefanovič | Olga Kurasova https://creativecommons.org/licenses/by/4.0
date: 2025-10-14
publication date: 2025-10-14
starting page: 1163
ending page: 1185
doi: 10.15388/namc.2025.30.43803

Boundary value problems for third-order differential equations involving singular Phi-Laplacian operators
type: item
description: We study strongly nonlinear, third-order differential equations of type (Φ(k(t)u''(t)))' = f(t, u(t), u'(t), u''(t)), a.e. t ∈ J, where Φ is the singular Φ-Laplacian operator. That is, Φ : (–r, r) -> R, r > 0, is a generic strictly increasing homeomorphism with bounded domain, which generalizes the relativistic operator Φ(u) := u (r2 – u2)–1/2. Moreover, k is a nonnegative continuous function, which can vanish on a set of zero measure, so such equations can be singular, and f is a general Carathédory function. For these equations, we investigate boundary value problems both in compact intervals (when J = [a; b]) and in a half-line (with J = [a;+∞)), and we prove existence results under mild assumptions. Our approach is based on fixed point techniques.
subject: Articles
  topic: section
subject: boundary value problems on unbounded domains
  topic: keywords
subject: heteroclinic solutions
  topic: keywords
subject: nonlinear differential operators
  topic: keywords
subject: singular Phi-Laplacian operator
  topic: keywords
subject: singular equation
  topic: keywords
creator: Alessandro Calamai
creator: Francesca Papalini
rights: Copyright (c) 2025 Alessandro Calamai | Francesca Papalini https://creativecommons.org/licenses/by/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 1145
ending page: 1162
doi: 10.15388/namc.2025.30.43775

Spatiotemporal dynamics of a modified Leslie–Gower predator–prey model: Effects of diffusion and taxis-driven movements on pattern formation
type: item
description: In this manuscript, we investigate a Leslie–Gower predator–prey model with Crowley–Martin-type functional response. We also explore the dynamics of reaction–diffusion as well as reaction–diffusion–advection model. Specifically, our study focuses on an ecological model involving a generalist predator that induces fear, has carry-over effects, and experiences competitive interference. For the temporal model, a detailed mathematical analysis is carried out, investigating the positivity and boundedness of the solutions. We observe both monostability and bistability phenomena, and explore various local and global bifurcations by varying the fear and carry-over parameters. Interestingly, the fear and its carry-over effects have opposing roles in influencing stability within the temporal model. We incorporated prey-taxis into a general reaction–diffusion framework to represent the directed movement of predators towards regions with higher prey densities or when tracking signals such as scent to locate their prey. We perform the complete analysis of diffusion-driven and taxis-driven instability for reaction–diffusion and reaction–diffusion–advection models, respectively. Our findings emphasize the significant influence of predator diffusion and prey-taxis on pattern formation, revealing that increased random predator movement, combined with a moderate level of prey-taxis, can stabilize the model.
subject: Articles
  topic: section
subject: fear effect
  topic: keywords
subject: carry-over effect
  topic: keywords
subject: bifurcations
  topic: keywords
subject: prey-taxis
  topic: keywords
subject: Turing pattern
  topic: keywords
creator: Anand Singh
creator: Sayan Mandal
creator: Pankaj Kumar Tiwari
creator: Balram Dubey
rights: Copyright (c) 2025 Anand Singh | Sayan Mandal | Pankaj Kumar Tiwari | Balram Dubey https://creativecommons.org/licenses/by/4.0
date: 2025-10-10
publication date: 2025-10-10
starting page: 1121
ending page: 1144
doi: 10.15388/namc.2025.30.43767

Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices
type: item
description: Arnold tongues of divergence in the Caputo fractional standard map of nilpotent matrices are explored in this paper. The scalar iterative variables in the Caputo fractional standard map are replaced by iterative matrix variables. The divergence effects induced by the nilpotent matrices result in specific patterns of Arnold tongues. Automatic machine classification techniques help to identify different types of Arnold tongues according to the dynamics of the transient processes of the system. Computational experiments are used to validate theoretical insights and to reveal the patterns of Arnold tongues of divergence.
subject: Articles
  topic: section
subject: Arnold tongue
  topic: keywords
subject: Caputo fractional standard map
  topic: keywords
subject: nilpotent, divergence
  topic: keywords
creator: Ugnė Orinaitė
creator: Rasa Šmidtaitė
creator: Minvydas Ragulskis
rights: Copyright (c) 2025 Ugnė Orinaitė | Rasa Šmidtaitė | Minvydas Ragulskis https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1103
ending page: 1120
doi: 10.15388/namc.2025.30.43746

Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation
type: item
description: This paper introduces novel fixed-point theorems for generalized Proinov contraction mappings utilizing the measure of noncompactness. These results significantly extend existing contraction principles and provide novel methods for analyzing nonlinear problems. We demonstrate the practical power of our theorems by establishing the existence of solutions to a broad class of nonlinear fractional differential equations with integral boundary conditions. An illustrative example underscores the effectiveness of our approach, promising impactful applications in fractional calculus and nonlinear analysis. Overall, these results enrich the theoretical framework and offer valuable insights for researchers working on complex dynamical systems and applied mathematical models.
subject: Articles
  topic: section
subject: Proinov-type contraction
  topic: keywords
subject: measure of noncompactness
  topic: keywords
subject: fractional differential equation
  topic: keywords
creator: Maha Belhadj
creator: Jamal Rezaei Roshan
creator: Stojan Stojan Radenović
rights: Copyright (c) 2025 Maha Belhadj | Jamal Rezaei Roshan | Stojan Stojan Radenović https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1081
ending page: 1102
doi: 10.15388/namc.2025.30.43745

Exploring fixed points via admissibility criteria for fuzzy theta f-weak contractions
type: item
description: In this study, we introduce a new class of fuzzy contractions, called fuzzy α-η-θf -weak contractions, and establish fixed point results within the framework of complete fuzzy metric spaces. A fuzzy metric space generalizes the concept of a metric space by defining the “distance” between two points ω and υ using a function ϑ(ω, υ, ς) that quantifies the degree of nearness between these points for a parameter ς > 0. This parameter ς reflects various factors influencing the closeness of the points, making fuzzy metric spaces a powerful tool for modeling uncertainty and imprecision in mathematical contexts. Based on this framework, we prove several fixed point theorems addressing the existence and uniqueness of fixed points for such contractions. By carefully selecting specific forms of the functions θf, α, and η, our primary results can be adapted to yield a variety of significant corollaries. Furthermore, our findings leverage admissible and auxiliary functions to provide a broader framework that consolidates, extends, and refines existing results in fixed point theory.
subject: Articles
  topic: section
subject: fixed point theory
  topic: keywords
subject: fuzzy metric
  topic: keywords
subject: contractions mapping
  topic: keywords
subject: admissible functions
  topic: keywords
subject: theta f-weak contraction
  topic: keywords
creator: Abdelhamid Moussaoui
rights: Copyright (c) 2025 Abdelhamid Moussaoui https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1067
ending page: 1080
doi: 10.15388/namc.2025.30.43744

Existence of nontrivial solutions for a class of 2n-order ODE
type: item
description: We consider a semilinear 2n-order problem with nonconstant coefficients. We deduce existence results by using variational methods in two directions. We primarily treat the existence when the nonlinearity has asymptotic linear behaviour at infinity and is either asymptotically sublinear or linear at zero. Secondly, we discuss the superlinear case at infinity and prove three existence results showing that our problem has at least one or two nonzero solutions.
subject: Articles
  topic: section
subject: higher-order equations
  topic: keywords
subject: variational methods
  topic: keywords
subject: critical points
  topic: keywords
creator: Antonia Chinnì
creator: Cristian-P. Danet
creator: Beatrice Di Bella
rights: Copyright (c) 2025 Antonia Chinnì | Cristian-P. Danet | Beatrice Di Bella https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1048
ending page: 1066
doi: 10.15388/namc.2025.30.43742

A new dynamic model for simultaneous saccharification and fermentation process of rice wine
type: item
description: In this paper, a new fractional model for the simultaneous saccharification and fermentation process of rice wine is proposed. To begin with, the existence and uniqueness of solution to the new model are proved by using some fixed point theorems. In addition, the stability at the equilibrium point and the Ulam–Hyers stability of the fractional simultaneous and saccharification fermentation model are analyzed. Then the approximate solutions of the fractional simultaneous saccharification and fermentation model are obtained by using the generalised Euler method. Finally, numerical simulations are given to verify the rationality of the fractional simultaneous saccharification and fermentation model. The new model proposed in this paper can more sensitively capture changes in the reaction.
subject: Articles
  topic: section
subject: simultaneous saccharification and fermentation
  topic: keywords
subject: fixed point theorem
  topic: keywords
subject: stability analysis
  topic: keywords
subject: generalized Euler method
  topic: keywords
subject: numerical simulation
  topic: keywords
creator: Li Wang
creator: Lihong Zhang
creator: Tingting Guan
rights: Copyright (c) 2025 Li Wang | Lihong Zhang | Tingting Guan https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1031
ending page: 1047
doi: 10.15388/namc.2025.30.43741

Efficient computation of blood velocity in the left atrial appendage: A practical perspective
type: item
description: The goal of the paper is to present the FSI (fluid-structure interaction) CFD (computational fluid dynamics) simulations of the blood flow in the LA (left atrium) for patient-specific geometry of the left atrium appendage (LAA). These simulations are important for the decision making in cardiology and cardiac surgery of the patients with atrial fibrillation. Nowadays according current atrial fibrillation treatment guidelines, initiation of oral anticoagulant therapy is recommended for patients with a CHA2DS2–VASc score greater or equal to 2 for males, and greater or equal to 3 for females, for lowering stroke risk. This therapy although has undesirable effects and provokes bleeding in a part of cases. That is why it is important to detect the stagnation zones of the blood flow in LAA. The presence of such zones justifies the necessity of the anticoagulant therapy. The FSI CFD simulations in the heart is a challenging problem: the existing softwares are not too robust for real life Reynolds numbers and often do not converge to the solution of the Navier–Stokes equations for the blood coupled with the elasticity equations of the wall. That is why we first provide the CFD computations with the rigid wall when the codes are more stable. Using this solution as a source of parameters for the implicit numerical scheme solver, we then provide the FSI computations, which become much more robust.
subject: Articles
  topic: section
subject: Navier–Stokes equations
  topic: keywords
subject: fluid structure interaction
  topic: keywords
subject: mathematical modeling
  topic: keywords
subject: computer simulations
  topic: keywords
creator: Audrius Aidietis
creator: Sigita Aidietienė
creator: Oleg Ardatov
creator: Sergejus Borodinas
creator: Rimgaudas Katkus
creator: Kristina Kaulakytė
creator: Nikolajus Kozulinas
creator: Grigory Panasenko
creator: Konstantinas Pileckas
creator: Gediminas Račkauskas
rights: Copyright (c) 2025 Audrius Aidietis | Sigita Aidietienė | Oleg Ardatov | Sergejus Borodinas | Rimgaudas Katkus | Kristina Kaulakytė | Nikolajus Kozulinas | Grigory Panasenko | Konstantinas Pileckas | Gediminas Račkauskas https://creativecommons.org/licenses/by/4.0
date: 2025-10-07
publication date: 2025-10-07
starting page: 1011
ending page: 1030
doi: 10.15388/namc.2025.30.43740

Background risk model in presence of heavy tails under dependence
type: item
description: In this paper, we examine two problems on applied probability, which are directly connected with the dependence in presence of heavy tails. The first problem is related to max-sum equivalence of the randomly weighted sums in bivariate setup. Introducing a new dependence, called generalized tail asymptotic independence, we establish the bivariate max-sum equivalence under a rather general dependence structure when the primary random variables follow distributions from the intersection of the dominatedly varying and the long-tailed distributions. Based on this max-sum equivalence, we provide a result about the asymptotic behavior of two kinds of ruin probabilities over a finite-time horizon in a bivariate renewal risk model with constant interest rate. The second problem is related to the asymptotic behavior of the tail distortion risk measure in a static portfolio called background risk model. In opposite to other approaches on this topic, we use a general enough assumption that is based on multivariate regular variation.
subject: Articles
  topic: section
subject: joint tail behavior
  topic: keywords
subject: randomly weighted sums
  topic: keywords
subject: tail distortion risk measure
  topic: keywords
subject: bivariate renewal risk model
  topic: keywords
subject: interdependence
  topic: keywords
subject: multivariate regular variation
  topic: keywords
creator: Dimitrios G. Konstantinides
creator: Charalampos D. Passalidis
rights: Copyright (c) 2025 Dimitrios G. Konstantinides | Charalampos D. Passalidis https://creativecommons.org/licenses/by/4.0
date: 2025-08-12
publication date: 2025-08-12
starting page: 982
ending page: 1010
doi: 10.15388/namc.2025.30.42995

Stability analysis of leptospirosis compartmental model with impact of contaminated environment
type: item
description: The main objective of this article is to analyse the stability properties of a model involving humans, animals and contaminated environment. As a first step, the model is formulated, and its biological well-posedness is proved. Then the basic reproduction number is derived using the next generation matrix (NGM) method. The local and global asymptotic stability of the system at the disease free and endemic equilibrium points are also established. Finally, numerical simulations to illustrate the validity of the theoretical results are performed.
subject: Articles
  topic: section
subject: leptospirosis
  topic: keywords
subject: free-living pathogen
  topic: keywords
subject: next-generation matrix method
  topic: keywords
subject: basic reproduction number
  topic: keywords
subject: stability analysis
  topic: keywords
creator: Mohandas Sooryadas
creator: Abdul Latheef Haseena
creator: Selvan Selsha
creator: Krishnan Balachandran
rights: Copyright (c) 2025 Mohandas Sooryadas | Abdul Latheef Haseena | Selvan Selsha | Krishnan Balachandran https://creativecommons.org/licenses/by/4.0
date: 2025-08-07
publication date: 2025-08-07
starting page: 957
ending page: 981
doi: 10.15388/namc.2025.30.42973

Finite-time synchronization and quasi-synchronization of fractional-order fuzzy BAM neural networks with time delays
type: item
description: This paper concentrates on the finite-time synchronization (FTS) and the quasi-synchronization (QS) problems for a kind of fractional-order fuzzy BAM neural networks with time delays (FOFBAMNNs). In order to reach the goals of synchronization, two novel controllers are designed. Then, based on finite-time stability theorem, Lyapunov function theory, and several inequality techniques, through the application of two different designed controllers, several criteria for both FTS and QS are established. Moreover, more precise error level and settling times are given. The effectiveness of the derived criteria is ultimately validated through two simulations.
subject: Articles
  topic: section
subject: finite-time synchronization
  topic: keywords
subject: quasi-synchronization
  topic: keywords
subject: BAM neural networks
  topic: keywords
subject: Caputo derivative
  topic: keywords
subject: fuzzy term.
  topic: keywords
creator: Wei Zhao
creator: Hongmei Zhang
creator: Hai Zhang
creator: Qinyun Lu
creator: Jinde Cao
rights: Copyright (c) 2025 Wei Zhao | Hongmei Zhang | Hai Zhang | Qinyun Lu | Jinde Cao https://creativecommons.org/licenses/by/4.0
date: 2025-07-30
publication date: 2025-07-30
starting page: 936
ending page: 956
doi: 10.15388/namc.2025.30.42902

On a novel semigroup of enriched Chatterjea-type mappings in Banach spaces with a numerical experiment
type: item
description: Recently in [V. Berinde and M. Păcurar, Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces, J. Fixed Point Theory Appl., 23(4):66, 2021], using the technique of enrichment of contractive mappings by Krasnoselskij averaging, Berinde and Păcurar introduced a new type of mappings, called enriched Chatterjea-type mappings. The main aim of this article is to introduce a new semigroup of enriched Chatterjea-type mappings. We also establish weak and strong convergence results for enriched Chatterjea-type semigroups using a novel iterative process in uniformly convex Banach spaces. To support the theoretical results, we conduct numerical experiments demonstrating the convergence behavior of the iterative scheme under various initial conditions and control sequences. The findings confirm exponential convergence and highlight the effectiveness and robustness of the proposed method for common fixed point approximation.
subject: Articles
  topic: section
subject: enriched Chatterjea-type mappings
  topic: keywords
subject: semigroups
  topic: keywords
subject: strong convergence
  topic: keywords
subject: weak convergence
  topic: keywords
creator: Thitima Kesahorm
creator: Wutiphol Sintunavarat
rights: Copyright (c) 2025 Thitima Kesahorm | Wutiphol Sintunavarat https://creativecommons.org/licenses/by/4.0
date: 2025-07-14
publication date: 2025-07-14
starting page: 913
ending page: 935
doi: 10.15388/namc.2025.30.42692

A revisit to tail risk measures in the presence of bivariate regularly varying tailed insurance and financial risks
type: item
description: Consider a discrete-time insurance risk model in which the one-period insurance and financial risks are assumed to be independent and identically distributed random pairs, but a strong dependence structure is allowed to exist between each pair. Recently, Q. Tang and Y. Yang employed a framework of bivariate regular variation to model the heavy tails and the dependence of the insurance and financial risks, and they also established an asymptotic formula for the finite-time ruin probability [Interplay of insurance and financial risks in a stochastic environment, Scand. Actuar. J., 2019(5):432–451, 2019]. In this paper, by adopting a different approach, we study the asymptotic behavior of some tail risk measures for the aggregate discounted net loss, including the tail probability and the conditional loss-based tail expectation. We show both analytically and numerically how the heavy tailedness and the dependence of each pair of insurance and financial risks affect the tail risk measures.
subject: Articles
  topic: section
subject: asymptotics
  topic: keywords
subject: aggregate discounted net loss
  topic: keywords
subject: insurance and financial risks
  topic: keywords
subject: tail risk measure
  topic: keywords
subject: bivariate regular variation
  topic: keywords
creator: Yang Yang
creator: Buyun Cheng
creator: Zhimin Zhang
rights: Copyright (c) 2025 Yang Yang | Buyun Cheng | Zhimin Zhang https://creativecommons.org/licenses/by/4.0
date: 2025-07-14
publication date: 2025-07-14
starting page: 892
ending page: 912
doi: 10.15388/namc.2025.30.42690

Numerical algorithms to solve one inverse problem for Navier–Stokes equations
type: item
description: This model describes the Poiseuille type solution in the nonstationary case of the Navier–Stokes problem. An equivalent form of PDE problem is defined as the first-kind Volterra integral equation. The main aim is to analyze a possible ill-posedness of the given problem. For some problems the first-kind Volterra integral equation can be modified to the integral equation of the second kind and the letter equation is well-posed. Different regularization techniques also can be used to control the influence of error pollution with not equal efficiency. Thus we made an extensive analysis and compared classical discretization schemes for PDE and integral Navier–Stokes models and regularization algorithms. The regularization methods are applied to control the influence of the noise in data. The numerical experiment was aimed at obtaining new information about the stability of schemes for the inverse problems. Different approximations methods are used to solve PDE and integral versions of the equation. Results of computational experiments are presented, they confirm the theoretical error analysis and stability estimates.
subject: Articles
  topic: section
subject: inverse problems
  topic: keywords
subject: numerical approximation
  topic: keywords
subject: Navier–Stokes problem
  topic: keywords
subject: Volterra equation
  topic: keywords
subject: regularization methods
  topic: keywords
creator: Raimondas Čiegis
rights: Copyright (c) 2025 Raimondas Čiegis https://creativecommons.org/licenses/by/4.0
date: 2025-07-01
publication date: 2025-07-01
starting page: 771
ending page: 791
doi: 10.15388/namc.2025.30.42686

Dynamic analysis of a fractional-order rumor spreading model with double time delay under higher-order interactions
type: item
description: Although traditional network-based models also explore higher-order interactions, they are limited in capturing the complex impacts of multibody interactions, making it difficult to characterize the reinforcement effect in rumor propagation. With this in mind, firstly, this study introduces the simplicial complexes, a higher-order mathematical tool, to model rumor propagation. Secondly, the fractional-order derivatives are employed to more accurately capture the memory effect and anomalous diffusion phenomenon in the rumor propagation process under higher-order interactions. Then propagation thresholds and the existence of model solutions are investigated. Moreover, the proposed model exhibits bistability, and the Hopf bifurcation is analysed by choosing time delay as the threshold. Numerical simulations suggest that fractional-order rumor spreading models with higher-order interactions are more consistent with actual data than network-based models and integer-order models.
subject: Articles
  topic: section
subject: rumor spreading
  topic: keywords
subject: fractional-order model
  topic: keywords
subject: higher-order interactions
  topic: keywords
subject: Hopf bifurcation
  topic: keywords
creator: Yang Xia
creator: Haijun Jiang
creator: Jiarong Li
creator: Shuzhen Yu
rights: Copyright (c) 2025 Yang Xia | Haijun Jiang | Jiarong Li | Shuzhen Yu https://creativecommons.org/licenses/by/4.0
date: 2025-06-27
publication date: 2025-06-27
starting page: 747
ending page: 770
doi: 10.15388/namc.2025.30.42681

A mathematical model for degradation of forest area by industrialization causing migration of wildlife species
type: item
description: This study presents a nonlinear mathematical model incorporating four key variables: forest area, biomass density, industrialization level, and wildlife population. The model assumes that biomass is proportional to forest area and that wildlife density depends on biomass availability. Our analysis demonstrates that increasing industrialization leads to significant forest depletion, which in turn accelerates wildlife migration. The results highlight critical thresholds beyond which forest degradation becomes irreversible, emphasizing the urgent need for sustainable industrial policies and conservation strategies. Numerical simulations and sensitivity analysis validate the model outcomes and provide insights for ecological preservation.
subject: Articles
  topic: section
subject: forest area
  topic: keywords
subject: industrialization
  topic: keywords
subject: migration
  topic: keywords
subject: wildlife species
  topic: keywords
subject: stability analysis
  topic: keywords
creator: Shikha Jatav
creator: Shyam Sundar
creator: Alok Malviya
rights: Copyright (c) 2025 Shikha Jatav | Shyam Sundar | Alok Malviya https://creativecommons.org/licenses/by/4.0
date: 2025-06-05
publication date: 2025-06-05
starting page: 874
ending page: 891
doi: 10.15388/namc.2025.30.42247

Analysis and exact solutions for reaction–diffusion predator–prey system with prey-taxis by phi6 method
type: item
description: This article analyses the biomathematical model that describes the reaction–diffusion predator–prey system with prey-taxis. The analysis includes addressing the question of whether the solution exists and is unique. The next goal is to obtain the exact solutions. The ɸ6 method has been utilized for this purpose. The simulations of the obtained solutions are also incorporated, providing a broader understanding of the solutions.
subject: Articles
  topic: section
subject: nonlinear fractional-order partial differential equations
  topic: keywords
subject: exact solutions
  topic: keywords
subject: phi6 method
  topic: keywords
creator: Rishi Naeem
creator: Muhammad Sajid Iqbal
creator: Ali Hasan Ali
creator: Mustafa Inc
rights: Copyright (c) 2025 Rishi Naeem | Muhammad Sajid Iqbal | Ali Hasan Ali | Mustafa Inc https://creativecommons.org/licenses/by/4.0
date: 2025-06-04
publication date: 2025-06-04
starting page: 732
ending page: 746
doi: 10.15388/namc.2025.30.42236

M-matrices and one-dimensional discrete Sturm–Liouville problems with nonlocal boundary conditions
type: item
description: This article is the second part of a survey dedicated to M-matrices and the application of the finite difference method to elliptic problems with nonlocal boundary conditions. Here, we examine cases in which the matrix of the resulting system of linear equations is an M-matrix. Here, we address the discrete Sturm–Liouville problem with nonlocal boundary conditions, describing its spectrum in one-dimensional case. This enables us to determine the values of the nonlocality parameters for which the finite difference scheme is represented by an M-matrix.
subject: Articles
  topic: section
subject: M-matrices
  topic: keywords
subject: finite-difference method
  topic: keywords
subject: Sturm–Liouville problem
  topic: keywords
subject: nonlocal boundary conditions
  topic: keywords
creator: Vytautas Būda
creator: Mifodijus Sapagovas
creator: Olga Štikonienė
creator: Artūras Štikonas
rights: Copyright (c) 2025 Vytautas Būda | Mifodijus Sapagovas | Olga Štikonienė | Artūras Štikonas https://creativecommons.org/licenses/by/4.0
date: 2025-07-01
publication date: 2025-07-01
starting page: 704
ending page: 731
doi: 10.15388/namc.2025.30.42210

A new class of integral-multipoint boundary value problems for nonlinear Hadamard fractional differential equations on a semiinfinite domain
type: item
description: In this paper, we introduce and investigate a new class of Hadamard fractional differential equation with integral-multipoint boundary conditions on a positive semiinfinite domain. We use the contraction mapping principle and the fixed point index theorem, respectively, to prove the uniqueness and the existence of at least two positive solutions to the given problem. Our results are new and enrich the literature on Hadamard-type fractional differential equations on unbounded domains. Some examples illustrating the main results are presented.
subject: Articles
  topic: section
subject: Hadamard fractional derivative
  topic: keywords
subject: contraction mapping principle
  topic: keywords
subject: fixed point index theorem
  topic: keywords
subject: positive solution
  topic: keywords
subject: unbounded domain
  topic: keywords
creator: Nemat Nyamoradi
creator: Bashir Ahmad
creator: Sotiris K. Ntouyas
rights: Copyright (c) 2025 Nemat Nyamoradi | Bashir Ahmad | Sotiris K. Ntouyas https://creativecommons.org/licenses/by/4.0
date: 2025-05-22
publication date: 2025-05-22
starting page: 850
ending page: 873
doi: 10.15388/namc.2025.30.42121

A class of nonlinear double-phase Dirichlet fractional differential equations
type: item
description: In this paper, we study the existence of positive solutions for a new class of double-phase Dirichlet fractional differential equations with singular and superlinear terms. By applying the Nehari manifold method we show that for all small values of the parameter τ > 0, the considered equation has at least two positive solutions.
subject: Articles
  topic: section
subject: psi-Hilfer fractional derivative
  topic: keywords
subject: double-phase problem
  topic: keywords
subject: positive solution
  topic: keywords
subject: singularity
  topic: keywords
creator: Shengda Zeng
creator: Jinxia Cen
creator: José Vanterler da C. Sousa
rights: Copyright (c) 2025 Shengda Zeng | Jinxia Cen | José Vanterler da C. Sousa https://creativecommons.org/licenses/by/4.0
date: 2025-05-21
publication date: 2025-05-21
starting page: 685
ending page: 703
doi: 10.15388/namc.2025.30.42116

Global dissipativity and quasi-Mittag-Leffler synchronization of fractional-order complex-valued neural networks with time delays and discontinuous activations
type: item
description: This paper explores fractional-order complex-valued neural networks (FOCVNNs) with time delays and discontinuous activation functions. A novel fractional-order inequality is utilized to study this system as a whole without dividing it into different components in the complex plane. Firstly, the existence of global Filippov solutions in the complex domain is proven by using the theories of vector norms and fractional calculus. Next, some sufficient conditions are derived to ensure the global dissipativity and quasi-Mittag-Leffler synchronization of FOCVNNs through the use of nonsmooth analysis and differential inclusion theory. The error bounds of quasi-Mittag-Leffler synchronization are also estimated without relying on the initial values. Finally, some numerical simulations are conducted to demonstrate the effectiveness of the presented findings.
subject: Articles
  topic: section
subject: dissipativity
  topic: keywords
subject: fractional-order complex-valued neural networks
  topic: keywords
subject: quasi-Mittag-Leffler synchronization
  topic: keywords
subject: time delays
  topic: keywords
subject: discontinuous activations
  topic: keywords
creator: Libo Wang
creator: Guigui Xu
rights: Copyright (c) 2025 Libo Wang | Guigui Xu https://creativecommons.org/licenses/by/4.0
date: 2025-05-14
publication date: 2025-05-14
starting page: 660
ending page: 684
doi: 10.15388/namc.2025.30.42006

Controllability of stochastic impulsive integro-differential systems involving nonlocal conditions and conformable derivatives
type: item
description: In this paper, the controllability of a stochastic impulsive integro-differential system involving nonlocal conditions and conformable derivatives is analyzed. The solution of the system is derived by Duhamel’s formula using Laplace and inverse Laplace transforms. The controllability result for the linear system is proved by using controllability Grammian matrix, and for the nonlinear integro-differential system, fixed point techniques are used. The applicability of the system is verified by means of an example.
subject: Articles
  topic: section
subject: controllability
  topic: keywords
subject: impulsive stochastic system
  topic: keywords
subject: integro-differential system
  topic: keywords
subject: conformable derivatives
  topic: keywords
subject: nonlocal conditions
  topic: keywords
creator: Ganesan Arthi
creator: Suresh Kumar Gopika
creator: Juan. J. Nieto
rights: Copyright (c) 2025 Ganesan Arthi | Suresh Kumar Gopika | Juan. J. Nieto https://creativecommons.org/licenses/by/4.0
date: 2025-05-13
publication date: 2025-05-13
starting page: 638
ending page: 659
doi: 10.15388/namc.2025.30.41988

Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws
type: item
description: This paper investigates the stability and dynamical behavior of soliton solutions in generalized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We establish the existence of stable multisoliton configurations using variational methods and demonstrate their stability under small perturbations through energy estimates and topological considerations. Furthermore, we explore topological invariants (particularly, the topological charge) in preventing certain types of instabilities and ensuring the long-term persistence of solitons.
subject: Articles
  topic: section
subject: soliton stability
  topic: keywords
subject: topological invariants
  topic: keywords
subject: nonlinear Klein–Gordon equation
  topic: keywords
subject: variational methods
  topic: keywords
creator: José Luis Díaz Palencia
rights: Copyright (c) 2025 José Luis Díaz Palencia https://creativecommons.org/licenses/by/4.0
date: 2025-05-12
publication date: 2025-05-12
starting page: 620
ending page: 637
doi: 10.15388/namc.2025.30.41967

Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach
type: item
description: This investigation focuses on the conformable time-fractional discrete coupled nonlinear Schrödinger system (CTFCDNLSEs). This system incorporates a fractional order represented as a conformable derivative. Through the application of the fractional transformation method (FTM), a set of novel analytical discrete solutions is derived. These solutions are characterized by an array of mathematical functions, including trigonometric, hyperbolic, and rational functions. Among these solutions, discrete fractional bright solitons, dark solitons, combined solitons, and periodic solutions stand out. To demonstrate the influence of the fractional-order parameter on the dynamics of fractional discrete solitons, graphical representations are provided. These findings are significant for exploring complex nonlinear discrete physical phenomena.
subject: Articles
  topic: section
subject: fractional transformation approach
  topic: keywords
subject: discrete soliton solution
  topic: keywords
subject: CTFCDNLSE
  topic: keywords
creator: Mostafa Eslami
rights: Copyright (c) 2025 Mostafa Eslami https://creativecommons.org/licenses/by/4.0
date: 2025-05-06
publication date: 2025-05-06
starting page: 606
ending page: 619
doi: 10.15388/namc.2025.30.41841

Finite-time stability of discrete fractional uncertain recurrent neural networks
type: item
description: This paper investigates finite-time stability of fractional uncertain difference equations with time delay. A fractional sum inequality is obtained from uncertain initial-value conditions. A delayed discrete Gronwall’s inequality is used, and sample paths are numerically illustrated. Finally, finite-time stability results are obtained for a fractional uncertain recurrent neural network model. It can be concluded that this paper provides an efficient tool for finite-time analysis of high-dimensional fractional uncertain systems with time delay.
subject: Articles
  topic: section
subject: fractional difference equations
  topic: keywords
subject: uncertainty distribution
  topic: keywords
subject: discrete Gronwall’s inequality
  topic: keywords
subject: time delay
  topic: keywords
creator: Lan-Lan Huang
creator: Guo-Cheng Wu
creator: Cheng Luo
rights: Copyright (c) 2025 Lan-Lan Huang | Guo-Cheng Wu | Cheng Luo https://creativecommons.org/licenses/by/4.0
date: 2025-05-03
publication date: 2025-05-03
starting page: 838
ending page: 849
doi: 10.15388/namc.2025.30.41799

Message spreading modeling from the perspective of social psychology, differential equation dynamics, and deep learning technique
type: item
description: To gain a deeper understanding of the characteristics of message spreading, it is crucial to explore various methods of modeling this phenomenon. Given that message spreading is significantly influenced by social media, we propose a modified spreading model informed by social psychology analysis. This approach also incorporates differential equation dynamics and deep learning technique. The proposed model accounts for a cross-transmission mechanism between individuals and social media platforms, as well as a nonlinear spreading rate, to effectively characterize the saturation effect of messages. Utilizing Lyapunov functionals, we carry out a dynamical analysis of the message spreading model. Furthermore, we develop physics-informed neural networks based on deep learning technique that merges the efficiency inherent in data-driven modeling with the precision offered by mathematical modeling. Numerical simulations demonstrate that our prediction method can accurately capture real-time changes in data while correcting deviations observed in data-driven predictions, which highlights the robust potential for multidisciplinary integration among social psychology, differential equation dynamics, and deep learning technique.
subject: Articles
  topic: section
subject: message spreading
  topic: keywords
subject: dynamical modeling
  topic: keywords
subject: deep learning technique
  topic: keywords
subject: social psychology
  topic: keywords
subject: cross-transmission mechanism
  topic: keywords
creator: Yuntao Li
creator: Yan Zhang
creator: Jiazhe Lin
rights: Copyright (c) 2025 Yuntao Li | Yan Zhang | Jiazhe Lin https://creativecommons.org/licenses/by/4.0
date: 2025-05-03
publication date: 2025-05-03
starting page: 592
ending page: 605
doi: 10.15388/namc.2025.30.41797

On well-posedness and decay of Active model B
type: item
description: We study the well-posedness and decay estimates of Cauchy problem for Active model B in R3. First, based on the higher-order norm estimates of solutions and the mollifier technique, we obtain the local existence of unique strong solution. Then, by using pure energy method, one proves the global well-posedness and time decay estimates, provided that the H3/2-norm of initial data is sufficiently small.
subject: Articles
  topic: section
subject: Active model B
  topic: keywords
subject: well-posedness
  topic: keywords
subject: decay rate
  topic: keywords
creator: Fengnan Liu
creator: Tong Wu
creator: Xiaopeng Zhao
rights: Copyright (c) 2025 Fengnan Liu | Tong Wu | Xiaopeng Zhao https://creativecommons.org/licenses/by/4.0
date: 2025-05-01
publication date: 2025-05-01
starting page: 573
ending page: 591
doi: 10.15388/namc.2025.30.41788