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 : 2026-01-28DOI: 10.1016/j.cnsns.2026.109793
Jie Chu, Yuejie Li, Minfu Feng, Zhendong Luo
{"title":"Two-grid reduced-dimension method and applications for the nonlinear single phase flow model coupled with ground stress in porous median","authors":"Jie Chu, Yuejie Li, Minfu Feng, Zhendong Luo","doi":"10.1016/j.cnsns.2026.109793","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109793","url":null,"abstract":"","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"44 1","pages":"109793"},"PeriodicalIF":3.9,"publicationDate":"2026-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146072044","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}
Pub Date : 2026-01-25DOI: 10.1016/j.cnsns.2026.109792
Bo Xu , Fan Wu , Jiang Zhou
This paper investigates the stability of the two-dimensional ideal magnetohydrodynamic equations with only horizontal dissipation. By exploiting the symmetry conditions imposed on the initial data and time-weighted energy estimates, we establish the global stability of this system near the background magnetic field (1,0) in the space H3. Furthermore, an algebraic decay rate of (u2, b2) is obtained in the H2 framework. The results reveal that the magnetic field introduces an additional smoothing effect, thereby stabilizing fluid motion.
{"title":"Stability of the ideal magnetohydrodynamic equations with horizontal dissipation","authors":"Bo Xu , Fan Wu , Jiang Zhou","doi":"10.1016/j.cnsns.2026.109792","DOIUrl":"10.1016/j.cnsns.2026.109792","url":null,"abstract":"<div><div>This paper investigates the stability of the two-dimensional ideal magnetohydrodynamic equations with only horizontal dissipation. By exploiting the symmetry conditions imposed on the initial data and time-weighted energy estimates, we establish the global stability of this system near the background magnetic field (1,0) in the space <em>H</em><sup>3</sup>. Furthermore, an algebraic decay rate of (<em>u</em><sub>2</sub>, <em>b</em><sub>2</sub>) is obtained in the <em>H</em><sup>2</sup> framework. The results reveal that the magnetic field introduces an additional smoothing effect, thereby stabilizing fluid motion.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109792"},"PeriodicalIF":3.8,"publicationDate":"2026-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047904","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 : 2026-01-24DOI: 10.1016/j.cnsns.2026.109790
Aiswarya T, Anurag Srijanani Prasad
This paper presents the construction of a hidden variable fractal interpolation function using Edelstein contractions in an iterated function system based on a finite collection of data points. The approach incorporates an iterated function system where variable functions act as vertical scaling factors leading to a generalised vector-valued fractal interpolation function. Furthermore, the paper rigorously examines the smoothness of the constructed function and establishes an upper bound for the box-counting dimension of its graph.
{"title":"Construction and Box-counting Dimension of the Edelstein Hidden Variable Fractal Interpolation Function","authors":"Aiswarya T, Anurag Srijanani Prasad","doi":"10.1016/j.cnsns.2026.109790","DOIUrl":"https://doi.org/10.1016/j.cnsns.2026.109790","url":null,"abstract":"This paper presents the construction of a hidden variable fractal interpolation function using Edelstein contractions in an iterated function system based on a finite collection of data points. The approach incorporates an iterated function system where variable functions act as vertical scaling factors leading to a generalised vector-valued fractal interpolation function. Furthermore, the paper rigorously examines the smoothness of the constructed function and establishes an upper bound for the box-counting dimension of its graph.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"4 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047905","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 : 2026-01-24DOI: 10.1016/j.cnsns.2026.109788
Akhtar Jan , Rehan Ali Shah , Ebraheem Alzahrani , Zehba Raizah
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 α, 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.
{"title":"Stochastic and fractional-order techniques for dynamics and stability of bi-enzymatic cooperative chemical reactions","authors":"Akhtar Jan , Rehan Ali Shah , Ebraheem Alzahrani , 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":"2026-01-24","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}
Pub Date : 2026-01-24DOI: 10.1016/j.cnsns.2026.109787
Jacek Gulgowski , Tomasz P. Stefański
In this paper, the theory of stability for fractional-order (FO) systems with response depending on an infinite time interval of history is presented for the first time. We propose a novel stability definition valid for linear FO systems described by the Marchaud derivative (equivalent to the Grünwald-Letnikov derivative) and a known time history of their state in the entire interval. Up to now, the problem of FO systems stability has been approached in simplified mathematical models based on the Riemann-Liouville and Caputo derivatives only or under the assumption of zero initial conditions when all the FO definitions (i.e. Riemann-Liouville, Caputo, Marchaud, Grünwald-Letnikov) are equivalent in terms of the Laplace transformation. This stems from the fact that such systems either require initial conditions defined at a single point only (similar to typical integer-order (IO) systems) or are initialized with zero values of the time-history interval. Hence their description from the stability point of view does not require proposing new definitions and can be obtained through a natural extension of the existing stability theory for IO systems. However, this does not allow for consistent mathematical modelling of the systems described by the FO derivative of Marchaud (Grünwald-Letnikov), which describes systems with an infinite memory of their state in time. The purpose of this paper is to fill this gap and propose the stability definition and the criterion valid for FO systems with response depending on an infinite time interval of history which offer mathematical methods and tools applicable in science and engineering.
{"title":"Stability of fractional-order systems using the Marchaud derivative with a response depending on an infinite time interval of history","authors":"Jacek Gulgowski , Tomasz P. Stefański","doi":"10.1016/j.cnsns.2026.109787","DOIUrl":"10.1016/j.cnsns.2026.109787","url":null,"abstract":"<div><div>In this paper, the theory of stability for fractional-order (FO) systems with response depending on an infinite time interval of history is presented for the first time. We propose a novel stability definition valid for linear FO systems described by the Marchaud derivative (equivalent to the Grünwald-Letnikov derivative) and a known time history of their state in the entire <span><math><mrow><mo>(</mo><mo>−</mo><mi>∞</mi><mo>,</mo><mn>0</mn><mo>]</mo></mrow></math></span> interval. Up to now, the problem of FO systems stability has been approached in simplified mathematical models based on the Riemann-Liouville and Caputo derivatives only or under the assumption of zero initial conditions when all the FO definitions (i.e. Riemann-Liouville, Caputo, Marchaud, Grünwald-Letnikov) are equivalent in terms of the Laplace transformation. This stems from the fact that such systems either require initial conditions defined at a single point only (similar to typical integer-order (IO) systems) or are initialized with zero values of the time-history interval. Hence their description from the stability point of view does not require proposing new definitions and can be obtained through a <em>natural</em> extension of the existing stability theory for IO systems. However, this does not allow for consistent mathematical modelling of the systems described by the FO derivative of Marchaud (Grünwald-Letnikov), which describes systems with an infinite memory of their state in time. The purpose of this paper is to fill this gap and propose the stability definition and the criterion valid for FO systems with response depending on an infinite time interval of history which offer mathematical methods and tools applicable in science and engineering.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"157 ","pages":"Article 109787"},"PeriodicalIF":3.8,"publicationDate":"2026-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146047907","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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