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.
{"title":"Theoretical and numerical study of exponential stability in thermo-poroelastic systems with tempered fractional delay","authors":"Luqman Bashir , Jianghao Hao , M. Fahim Aslam , 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":"2026-01-29","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}
Pub Date : 2026-01-29DOI: 10.1016/j.cnsns.2026.109810
Ibrahim Dahi , Moulay Rchid Sidi Ammi , Mostafa Tahiri , Delfim F.M. Torres
In this paper, we examine a broader variant of the nonlocal thermistor problem, which the heat diffusion that occurs when an electric current flows through a substance. which characterizes the heat diffusion phenomenon that occurs when an electric current flows through a substance. We analyze the doubly nonlinear problem in which the equation describing the temperature evolution has a nonlocal term on the right-hand side whereasthe first nonlinearity is present in the diffusion term. By virtue of an approximation technique, we establish the existence and uniqueness of a global weak solution to the considered problem in Sobolev spaces.Using the finite-difference approach, this paper offers a useful summary of numerical solutions in two dimensions to the non-local thermistor problem. The analysis includes a rigorous error estimation and is supported by numerical experiments that confirm the effectiveness and robustness of the proposed scheme, demonstrating second-order convergence in space as well as first-order convergence in time.
{"title":"On the well-posedness and numerical approximation of a nonlocal thermistor problem","authors":"Ibrahim Dahi , Moulay Rchid Sidi Ammi , Mostafa Tahiri , Delfim F.M. Torres","doi":"10.1016/j.cnsns.2026.109810","DOIUrl":"10.1016/j.cnsns.2026.109810","url":null,"abstract":"<div><div>In this paper, we examine a broader variant of the nonlocal thermistor problem, which the heat diffusion that occurs when an electric current flows through a substance. which characterizes the heat diffusion phenomenon that occurs when an electric current flows through a substance. We analyze the doubly nonlinear problem in which the equation describing the temperature evolution has a nonlocal term on the right-hand side whereasthe first nonlinearity is present in the diffusion term. By virtue of an approximation technique, we establish the existence and uniqueness of a global weak solution to the considered problem in Sobolev spaces.Using the finite-difference approach, this paper offers a useful summary of numerical solutions in two dimensions to the non-local thermistor problem. The analysis includes a rigorous error estimation and is supported by numerical experiments that confirm the effectiveness and robustness of the proposed scheme, demonstrating second-order convergence in space as well as first-order convergence in time.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109810"},"PeriodicalIF":3.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072035","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}
Pub Date : 2026-01-29DOI: 10.1016/j.cnsns.2026.109795
Jianguo Si , Xinyu Guan
This paper is devoted to studying the existence of analytic solutions to a class of nonlinear differential equations with multiple proportional delays (see (1.4) in introduction). Firstly, we give the sufficient conditions for the existence of the analytic solutions near an ordinary point when the equation is a retarded type or a neutral type. Next, for a special case of this equation (see (1.7) in introduction), we prove that it has a special form of power series solution near a regular singular point. Finally, for several special cases of this equation considered in this paper we perform numerical simulations. The method used in this paper is the classical majorant series method. According to the position of the proportional delay multiplier q on the complex plane, the convergence of the formal solution is proved by constructing the majorant series of the formal solution. Especially, when q is on the unit circle but not a root of the unity, the proofs involve some techniques to handle small divisor problems including the application of Davie’s lemma.
{"title":"Construction of analytic solutions to nonlinear differential equations with multiple proportional delays","authors":"Jianguo Si , Xinyu Guan","doi":"10.1016/j.cnsns.2026.109795","DOIUrl":"10.1016/j.cnsns.2026.109795","url":null,"abstract":"<div><div>This paper is devoted to studying the existence of analytic solutions to a class of nonlinear differential equations with multiple proportional delays (see (1.4) in introduction). Firstly, we give the sufficient conditions for the existence of the analytic solutions near an ordinary point <span><math><mrow><mi>z</mi><mo>=</mo><mn>0</mn></mrow></math></span> when the equation is a retarded type or a neutral type. Next, for a special case of this equation (see (1.7) in introduction), we prove that it has a special form of power series solution near a regular singular point. Finally, for several special cases of this equation considered in this paper we perform numerical simulations. The method used in this paper is the classical majorant series method. According to the position of the proportional delay multiplier <em>q</em> on the complex plane, the convergence of the formal solution is proved by constructing the majorant series of the formal solution. Especially, when <em>q</em> is on the unit circle but not a root of the unity, the proofs involve some techniques to handle small divisor problems including the application of Davie’s lemma.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109795"},"PeriodicalIF":3.8,"publicationDate":"2026-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072034","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}
Pub Date : 2026-01-28DOI: 10.1016/j.cnsns.2026.109796
Ulises Chialva , Walter Reartes
We study the control of chaotic dynamics in the hybrid Nakano-Saito oscillator through periodic resetting schemes. In contrast to most existing approaches, which rely on Lyapunov-based constructions or optimization-driven control strategies, we focus on the underlying dynamical mechanisms responsible for the emergence of controlled and uncontrolled regimes. By analyzing the associated impact (return) map, we identify well-defined control windows that give rise to stable periodic solutions and investigate their dependence on the ratio γ between the oscillator’s natural frequency and the control frequency. We provide an analytical proof for the existence of a limit cycle and use this result to characterize the main control windows of the system, revealing distinct bifurcation phenomena that enable different regimes of chaos control within this canonical hybrid framework. Finally, we examine a stochastic resetting protocol governed by an inverse Gaussian distribution and show that it can outperform deterministic control schemes subject to timing jitter, achieving enhanced stabilization. These results demonstrate that classical dynamical systems tools are sufficient to derive precise control conditions and to assess control effectiveness even in stochastic hybrid settings.
{"title":"Chaos control and stabilization of a hybrid chaotic oscillator through deterministic and stochastic resets","authors":"Ulises Chialva , Walter Reartes","doi":"10.1016/j.cnsns.2026.109796","DOIUrl":"10.1016/j.cnsns.2026.109796","url":null,"abstract":"<div><div>We study the control of chaotic dynamics in the hybrid Nakano-Saito oscillator through periodic resetting schemes. In contrast to most existing approaches, which rely on Lyapunov-based constructions or optimization-driven control strategies, we focus on the underlying dynamical mechanisms responsible for the emergence of controlled and uncontrolled regimes. By analyzing the associated impact (return) map, we identify well-defined control windows that give rise to stable periodic solutions and investigate their dependence on the ratio <em>γ</em> between the oscillator’s natural frequency and the control frequency. We provide an analytical proof for the existence of a limit cycle and use this result to characterize the main control windows of the system, revealing distinct bifurcation phenomena that enable different regimes of chaos control within this canonical hybrid framework. Finally, we examine a stochastic resetting protocol governed by an inverse Gaussian distribution and show that it can outperform deterministic control schemes subject to timing jitter, achieving enhanced stabilization. These results demonstrate that classical dynamical systems tools are sufficient to derive precise control conditions and to assess control effectiveness even in stochastic hybrid settings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109796"},"PeriodicalIF":3.8,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071595","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}
Pub Date : 2026-01-28DOI: 10.1016/j.cnsns.2026.109785
Grace Nnennaya Ogwo , Habib ur Rehman , Jen-Chih Yao
In this paper, we investigate the variational inequality problem with fixed-point constraints. We propose and analyze an inertial subgradient extragradient method for approximating a common solution to a quasimonotone variational inequality problem and a fixed-point problem of an infinite family of relatively nonexpansive mappings. The study is conducted in the context of a real 2-uniformly convex and uniformly smooth Banach space. Under standard assumptions, we establish a strong convergence result. Finally, we provide numerical experiments to demonstrate the effectiveness and applicability of the proposed method. Our results complement several existing methods in the literature.
{"title":"Inertial subgradient–extragradient schemes for variational inequalities in 2-uniformly convex spaces","authors":"Grace Nnennaya Ogwo , Habib ur Rehman , Jen-Chih Yao","doi":"10.1016/j.cnsns.2026.109785","DOIUrl":"10.1016/j.cnsns.2026.109785","url":null,"abstract":"<div><div>In this paper, we investigate the variational inequality problem with fixed-point constraints. We propose and analyze an inertial subgradient extragradient method for approximating a common solution to a quasimonotone variational inequality problem and a fixed-point problem of an infinite family of relatively nonexpansive mappings. The study is conducted in the context of a real 2-uniformly convex and uniformly smooth Banach space. Under standard assumptions, we establish a strong convergence result. Finally, we provide numerical experiments to demonstrate the effectiveness and applicability of the proposed method. Our results complement several existing methods in the literature.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109785"},"PeriodicalIF":3.8,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072060","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}
Pub Date : 2026-01-28DOI: 10.1016/j.cnsns.2026.109803
Yonghong Chen , Shoucheng Yuan , Xiaoqiu Lv , Jun Cheng , Jinde Cao
This paper explores probability-based dynamic event-triggered security control for fuzzy systems with nonhomogeneous sojourn probabilities (NSPs). A novel framework for NSP-based fuzzy systems is developed using a deterministic signal to accurately capture dynamic behavior, thereby overcoming the challenge of estimating mode transition probabilities. Considering the stochastic nature of network-induced delays, a new probability-based dynamic event-triggered protocol is proposed, where the threshold function is mode-dependent and adapts probabilistically. Additionally, to address delay segmentation and deception attacks effectively, a flexible protocol-based fuzzy control law is introduced, leveraging probability distribution information. Finally, the theoretical findings are validated through simulation experiments using a mass-spring mechanical model, confirming their effectiveness and practical applicability.
{"title":"Protocol-Based security control for fuzzy systems with nonhomogeneous sojourn probabilities","authors":"Yonghong Chen , Shoucheng Yuan , Xiaoqiu Lv , Jun Cheng , Jinde Cao","doi":"10.1016/j.cnsns.2026.109803","DOIUrl":"10.1016/j.cnsns.2026.109803","url":null,"abstract":"<div><div>This paper explores probability-based dynamic event-triggered security control for fuzzy systems with nonhomogeneous sojourn probabilities (NSPs). A novel framework for NSP-based fuzzy systems is developed using a deterministic signal to accurately capture dynamic behavior, thereby overcoming the challenge of estimating mode transition probabilities. Considering the stochastic nature of network-induced delays, a new probability-based dynamic event-triggered protocol is proposed, where the threshold function is mode-dependent and adapts probabilistically. Additionally, to address delay segmentation and deception attacks effectively, a flexible protocol-based fuzzy control law is introduced, leveraging probability distribution information. Finally, the theoretical findings are validated through simulation experiments using a mass-spring mechanical model, confirming their effectiveness and practical applicability.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109803"},"PeriodicalIF":3.8,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072069","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}
Pub Date : 2026-01-27DOI: 10.1016/j.cnsns.2026.109798
Yuanyuan Liu, Seifu Neda Tereda, Zhexin Wen
This article presents a stochastic tritrophic food chain model integrating fear-induced behavioral changes and Markov regime switching to capture environmental variability. We prove the existence of a unique global positive solution and derive a threshold condition, based on stochastic boundary processes, that governs the persistence or extinction of species under random perturbations. Our theoretical results are further supported by numerical simulations conducted using the tamed Milstein method, which overcomes the limitations of standard schemes. The findings offer valuable insights for ecological modeling, demonstrating that incorporating behavioral responses and stochasticity can have a significant impact on species dynamics.
{"title":"Dynamics of fear effect on a stochastic tritrophic level food chain model with Markov switching","authors":"Yuanyuan Liu, Seifu Neda Tereda, Zhexin Wen","doi":"10.1016/j.cnsns.2026.109798","DOIUrl":"10.1016/j.cnsns.2026.109798","url":null,"abstract":"<div><div>This article presents a stochastic tritrophic food chain model integrating fear-induced behavioral changes and Markov regime switching to capture environmental variability. We prove the existence of a unique global positive solution and derive a threshold condition, based on stochastic boundary processes, that governs the persistence or extinction of species under random perturbations. Our theoretical results are further supported by numerical simulations conducted using the tamed Milstein method, which overcomes the limitations of standard schemes. The findings offer valuable insights for ecological modeling, demonstrating that incorporating behavioral responses and stochasticity can have a significant impact on species dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109798"},"PeriodicalIF":3.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146071521","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}
Pub Date : 2026-01-27DOI: 10.1016/j.cnsns.2026.109794
Kunlun Huang , Xintian Jia , Yanqi Zhang , Ya Li , Cuiping Li
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.
{"title":"Bifurcation and chaos in a discrete-time predator-prey system with strong Allee effect","authors":"Kunlun Huang , Xintian Jia , Yanqi Zhang , Ya Li , 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":"2026-01-27","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}
To address the inherent narrow-bandwidth limitation of conventional linear energy harvesting, this study proposes a nonlinear fluid-structure interaction (FSI) energy harvester based on a bimorph pipe conveying fluid constrained by retaining clips, which introduces two distinct nonlinear mechanisms: i) boundary nonlinearity due to the equivalent nonlinear stiffness, and ii) geometric nonlinearity from the extensible centerline of the pipe. The electro-mechanical governing equations of such nonlinear FSI system are established via the Hamilton principle, whereby the complex eigenfrequencies are first obtained for stability analysis. The vibration and electrical responses are further attained to evaluate the energy harvesting performance. In particular, a novel supercritical analysis is conducted to predict the harvester behaviour under buckling and flutter instabilities. Numerical results demonstrate that the designed nonlinear harvester significantly improves the operational bandwidth, and its performance can be regulated by tuning various system parameters. Interestingly, the FSI effect contributes to a broader energy harvesting bandwidth in the low-frequency region, but leads to a reduced peak voltage in the flutter state. In addition to force excitation, displacement excitation is also concerned, under which a better energy harvesting performance is exhibited. However, high nonlinear stiffness in this pattern may result in numerical divergence.
{"title":"Nonlinear energy harvesting of a piezoelectric pipe conveying fluid integrating boundary and geometric nonlinearities","authors":"Feng Liang , Tian-Chi Yu , Yao Chen , Xiao-Tian Guo","doi":"10.1016/j.cnsns.2026.109799","DOIUrl":"10.1016/j.cnsns.2026.109799","url":null,"abstract":"<div><div>To address the inherent narrow-bandwidth limitation of conventional linear energy harvesting, this study proposes a nonlinear fluid-structure interaction (FSI) energy harvester based on a bimorph pipe conveying fluid constrained by retaining clips, which introduces two distinct nonlinear mechanisms: i) boundary nonlinearity due to the equivalent nonlinear stiffness, and ii) geometric nonlinearity from the extensible centerline of the pipe. The electro-mechanical governing equations of such nonlinear FSI system are established via the Hamilton principle, whereby the complex eigenfrequencies are first obtained for stability analysis. The vibration and electrical responses are further attained to evaluate the energy harvesting performance. In particular, a novel supercritical analysis is conducted to predict the harvester behaviour under buckling and flutter instabilities. Numerical results demonstrate that the designed nonlinear harvester significantly improves the operational bandwidth, and its performance can be regulated by tuning various system parameters. Interestingly, the FSI effect contributes to a broader energy harvesting bandwidth in the low-frequency region, but leads to a reduced peak voltage in the flutter state. In addition to force excitation, displacement excitation is also concerned, under which a better energy harvesting performance is exhibited. However, high nonlinear stiffness in this pattern may result in numerical divergence.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"158 ","pages":"Article 109799"},"PeriodicalIF":3.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072048","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}
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