Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Secure containment control for switched nonlinear stochastic multi-agent systems under denial of service attacks","authors":"Jie Kong ,&nbsp;Bo Zhao","doi":"10.1016/j.cnsns.2026.109800","DOIUrl":"10.1016/j.cnsns.2026.109800","url":null,"abstract":"<div><div>This article investigates the secure containment control problem for switched nonlinear stochastic multi-agent systems (MASs) by using the mode-dependent average dwell time (MDADT) method. As a class of cyber-physical systems, MASs are vulnerable to denial of service (DoS) attacks, which can greatly degrade the control performance or even influence the stability of controlled systems. By combining the backstepping method, a secure containment control method is developed with the event-triggering mechanism. Based on the connectivity information between communication links, this method eliminates the effects of DoS attacks. In the backstepping recursive design process, the problem of “explosion of complexity” caused by the derivation of virtual control is addressed by introducing a command filter. Additionally, the event-triggering mechanism is designed in the backstepping process to effectively save the communication resources. Then, the event-triggered secure containment control policy is derived to ensure the stability of single follower and MASs under synchronous and asynchronous switchings. The followers led by multiple leaders eventually enter and keep moving in the convex hull composed of leaders. A simulation example demonstrates the effectiveness of the present secure containment control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109800"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Periodic wave propagation of a discrete diffusive vector-borne epidemic model in spatially periodic patchy environment","authors":"Xibei Jiang,&nbsp;Weixin Wu","doi":"10.1016/j.cnsns.2026.109815","DOIUrl":"10.1016/j.cnsns.2026.109815","url":null,"abstract":"<div><div>In this paper, a discrete diffusive vector-borne epidemic model in a spatially periodic patchy environment is proposed. That is, in this discrete model, all parameters exhibit periodic changes with period <em>N</em>. We establish the basic reproduction number <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> and the critical wave speed <em>c</em>*. By the upper and lower-solution method and Schauder’s fixed theorem, the existence of periodic traveling wave solutions satisfying specific boundary conditions is established when <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> and <em>c</em> ≥ <em>c</em>*. Additionally, the asymptotic behaviors of traveling wave solutions are given by the asymptotic spreading speed theory. By employing eigenvalue analysis of the linearized system with comparison principles, the non-existence of traveling wave solutions is established when <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span> or <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>&lt;</mo><msup><mi>c</mi><mo>*</mo></msup></mrow></math></span>. The numerical simulation eventually verified the correctness of the theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109815"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146110506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability and error estimates of a second-order decoupled finite element method for the time-dependent Stokes-Biot problem","authors":"Liming Guo,&nbsp;Shishun Li","doi":"10.1016/j.cnsns.2026.109806","DOIUrl":"10.1016/j.cnsns.2026.109806","url":null,"abstract":"<div><div>In this paper, we propose a second-order in time decoupled finite element method for the time-dependent Stokes-Biot problem. Our numerical scheme is a combination of the second-order backward differentiation formula and the second-order Gear’s extrapolation approach. It uncouples the original problem into two decoupled problems, the Stokes model and the Biot model. We establish the stability of the proposed fully-discrete finite element scheme in both the <em>L</em>²-norm and the <em>H</em>¹-norm, and derive the corresponding error estimates. Numerical results show that our algorithm delivers faster computation and lower memory usage than monolithic methods while maintaining comparable accuracy.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109806"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Theoretical and numerical study of exponential stability in thermo-poroelastic systems with tempered fractional delay","authors":"Luqman Bashir ,&nbsp;Jianghao Hao ,&nbsp;M. Fahim Aslam ,&nbsp;Iqra Kanwal","doi":"10.1016/j.cnsns.2026.109808","DOIUrl":"10.1016/j.cnsns.2026.109808","url":null,"abstract":"<div><div>We study a thermo–poroelastic system of coupled equations that incorporates a tempered Caputo fractional operator acting on a time–varying delay, extending previous models by including these effects. Under appropriate structural and dissipativity conditions, we establish well–posedness and prove exponential stability of the associated energy functional. A numerical scheme is constructed and tested, confirming the predicted decay rates and illustrating the influence of poroelastic damping, thermo–mechanical coupling and fractional parameters. The results show consistent agreement between theory and computation and to the best of our knowledge, this is a significant extension of previous studies in control or wave–type PDE systems, where a tempered Caputo derivative acts on a time–varying delay.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109808"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Differentiable minimization problems for variational-hemivariational inequalities","authors":"Rong Hu ,&nbsp;Dong-Ling Cai ,&nbsp;Yi-Bin Xiao ,&nbsp;Wei Li","doi":"10.1016/j.cnsns.2026.109805","DOIUrl":"10.1016/j.cnsns.2026.109805","url":null,"abstract":"<div><div>In this paper, we propose a family of Moreau-Yosida regularized gap functions for variational-hemivariational inequalities, based on generalized gradients of locally Lipschitz functions. We show that the original problem is equivalent to an unconstrained, convex and continuously differentiable minimization problem. In addition, we establish global error bounds and derive a Polyak-Łojasiewicz inequality with explicit constants, which yields linear convergence of standard first-order methods. Numerical simulations are presented to illustrate the theoretical results and the predicted convergence behavior.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109805"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation and chaos in a discrete-time predator-prey system with strong Allee effect","authors":"Kunlun Huang ,&nbsp;Xintian Jia ,&nbsp;Yanqi Zhang ,&nbsp;Ya Li ,&nbsp;Cuiping Li","doi":"10.1016/j.cnsns.2026.109794","DOIUrl":"10.1016/j.cnsns.2026.109794","url":null,"abstract":"<div><div>A discrete-time system incorporating a strong Allee effect, derived by discretizing the corresponding continuous predator-prey model via the Euler method, is analyzed. Stability analysis reveals that when the predator mortality rate exceeds a critical threshold, two interior equilibria emerge, enabling coexistence of both species. Bifurcation analysis further demonstrates that the system may undergo flip and Neimark-Sacker bifurcations in response to parameter variations. The findings indicate that a strong Allee effect stabilizes the system by generating stable equilibrium points, whereas a weak Allee effect can induce more complex dynamics, such as periodic orbits and chaotic attractors. Additionally, the results highlight the system’s high sensitivity to ecological parameters, including predator population growth rate and environmental protection measures.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109794"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of semilinear fractional integro-differential equations governed by compact semigroups","authors":"Mohammad H.M. Rashid","doi":"10.1016/j.cnsns.2026.109789","DOIUrl":"10.1016/j.cnsns.2026.109789","url":null,"abstract":"<div><div>This paper investigates the existence and qualitative properties of mild solutions to semilinear fractional integro-differential equations in Banach spaces of the form<span><span><span><math><mrow><msup><mrow></mrow><mi>c</mi></msup><msubsup><mi>D</mi><mi>t</mi><mi>α</mi></msubsup><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mi>A</mi><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mo>∫</mo><mrow><mn>0</mn></mrow><mi>t</mi></msubsup><mi>K</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>s</mi><mo>)</mo></mrow><mi>g</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>)</mo></mrow><mi>d</mi><mi>s</mi><mo>)</mo></mrow></mrow></math></span></span></span>with initial condition <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><msub><mi>u</mi><mn>0</mn></msub></mrow></math></span>, where <span><math><mrow><msup><mrow></mrow><mi>c</mi></msup><msubsup><mi>D</mi><mi>t</mi><mi>α</mi></msubsup></mrow></math></span> denotes the Caputo fractional derivative of order <em>α</em> ∈ (0, 1), <em>A</em> generates a compact <em>C</em>₀-semigroup {<em>T</em>(<em>t</em>)}_{<em>t</em> ≥ 0} on a Banach space <em>X</em>, and <em>f, g</em> are continuous nonlinear functions with <em>K</em> being a continuous kernel. Using compact semigroup theory and various fixed point theorems, including Schauder’s and Banach’s fixed point theorems, we establish several local existence results for mild solutions under different regularity and growth conditions on the nonlinearities. Furthermore, we explore global existence and blow-up phenomena, proving that solutions exist globally under appropriate dissipativity conditions, growth restrictions, or when the nonlinearities satisfy critical Osgood-type conditions. The paper also provides illustrative examples that demonstrate the applicability of our theoretical results to concrete fractional integro-differential problems, particularly in the context of partial differential equations with fractional time derivatives.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109789"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146095738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic and fractional-order techniques for dynamics and stability of bi-enzymatic cooperative chemical reactions","authors":"Akhtar Jan ,&nbsp;Rehan Ali Shah ,&nbsp;Ebraheem Alzahrani ,&nbsp;Zehba Raizah","doi":"10.1016/j.cnsns.2026.109788","DOIUrl":"10.1016/j.cnsns.2026.109788","url":null,"abstract":"<div><div>The cell has a highly organized system where enzymes catalyze complex biochemical reactions. Given the inherently complex nature of these reactions, this work examines the dynamics and stability of a fractional-order enzymatic reaction model by introducing memory effects and stochastic fluctuations. The first step involves converting the non-linear differential equations in a fractional-order system into a stochastic model by applying the Grünwald-Letnikov (GL) operator, thereby incorporating random fluctuations into the system. The model is analyzed using three complementing approaches: the Euler-Maruyama technique, the Homotopy Perturbation Method (HPM), and the Laplace Adomian Decomposition Method (LADM). Both quantitative and qualitative calculations of the results’ positivity, boundedness, uniqueness, and convergence are examined. To validate the system’s stability analysis, Picard’s stability criteria and the fixed-point theorem are used. The system is numerically simulated for different values of fractional orders, and the error evaluation between LADM and HPM is analyzed and validated using their graphs and tables. The results show that system stability is strongly affected by the fractional-order parameter <em>α</em>, causing unstable conditions that disturb reaction kinetics. LADM’s high accuracy and convergence allow for a solid analytical approximation to fractional differential equations, whereas HPM is simpler to learn but less effective at demonstrating long-term memory effects. The stochastic analysis highlights the need to include randomness in models for more accurate predictions and shows how biochemical noise affects enzyme activity. The findings state the importance of fractional calculus in the study of enzyme activity and set a direction for future research in industrial and biochemical applications.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109788"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Credit risk for large portfolios of green and brown loans: Extending the ASRF model","authors":"Alessandro Ramponi,&nbsp;Sergio Scarlatti","doi":"10.1016/j.cnsns.2026.109750","DOIUrl":"10.1016/j.cnsns.2026.109750","url":null,"abstract":"<div><div>Inspired by the classical Vasicek approach to credit risk, we propose an extended model for portfolios composed of green and brown loans, widening the Asymptotic Single Risk Factor framework via a two-factor copula structure. Systematic risk is modeled using potentially skewed distributions, allowing for asymmetric creditworthiness effects, while idiosyncratic risk remains Gaussian. Under a non-uniform exposure setting, we establish convergence in quadratic mean of the portfolio loss to a limit reflecting the distinct characteristics of the two loan segments. Numerical results confirm the theoretical findings and illustrate how value-at-risk is affected by portfolio granularity, default probabilities, factor loadings, and skewness. Our model accommodates differential sensitivity to systematic shocks and offers a tractable basis for further developments in credit risk modeling, including granularity adjustments, collateralized default obligations pricing, and empirical analysis of green loan portfolios.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109750"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Novel subgradient extragradient methods for equilibrium problems in Hilbert spaces","authors":"Pham Ky Anh ,&nbsp;Ngo Thi Thuong ,&nbsp;Nguyen The Vinh","doi":"10.1016/j.cnsns.2026.109777","DOIUrl":"10.1016/j.cnsns.2026.109777","url":null,"abstract":"<div><div>In this paper, by combining the inertial technique and subgradient extragradient method with a new strategy of stepsize selection, we propose a novel extragradient-type method to solve pseudomonotone equilibrium problems in real Hilbert spaces. Our method is designed such that the stepsize sequence is increasing after a finite number of iterations. This distinguishes our method from most other extragradient-type methods for equilibrium problems. The weak and strong convergence of new algorithms under standard assumptions are established. We examine the performance of our methods on the Nash-Cournot oligopolistic equilibrium models of electricity markets. The reported numerical results demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109777"},"PeriodicalIF":3.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146033542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}