Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Exponential stability of fractional order impulsive switched system with stable and unstable subsystems","authors":"Qinqin Liao,&nbsp;Danfeng Luo","doi":"10.1016/j.cnsns.2025.108940","DOIUrl":"10.1016/j.cnsns.2025.108940","url":null,"abstract":"<div><div>The exponential stability of the Caputo fractional order impulsive switched system (CFOISS) consisting of stable and unstable subsystems is addressed in this paper. We integrate the multiple Lyapunov function (MLFs) approach, the mode-dependent average dwell time (MDADT) method, and the fast-slow switching concept to handle the switched sequence. In order to better represent the impulse, we further employ the mode-dependent average impulsive interval (MDAII) technique to process the impulsive sequence. The relationship between impulsive intensity, system mode, MDADT and MDAII is successfully established by considering the synchronization and complete asynchronism of impulse and switched time, respectively, and a set of low conservative sufficient conditions is derived. The results show that CFOISS can achieve exponential stability under certain switching rule when the state trajectory can be compensated by the slow switching stable subsystem for the impact of the quick switching unstable subsystem, and the jump of the impulsive point is within a certain range. Finally, the stability of the proposed method is verified by several numerical simulation examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108940"},"PeriodicalIF":3.4,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125016","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":"Suppression of vortex-induced vibrations using bistable nonlinear energy sink","authors":"Sudipta Maity ,&nbsp;B. Santhosh ,&nbsp;Bipin Balaram ,&nbsp;Jan Awrejcewicz","doi":"10.1016/j.cnsns.2025.108952","DOIUrl":"10.1016/j.cnsns.2025.108952","url":null,"abstract":"<div><div>The use of conventional cubic nonlinear energy sink (NES) to mitigate vortex-induced vibrations has been widely investigated. Recently, bistable NES (BNES) has gained considerable attention owing to its ability to execute large amplitude inter-well motion and thus enhance energy transfer. But, the efficacy of BNES to mitigate self-excited vibrations in general and vortex-induced self-excited vibrations in particular seems to have received little interest. The present study proposes the use of BNES to mitigate the vibration of an elastically mounted circular cylinder subjected to a flow field. The van der Pol equation with acceleration coupling is used to model the wake behavior. The BNES is appended to the linear structure. Analytical and numerical investigations are performed to understand the mechanism of energy transfer and to demonstrate the advantages of BNES over conventional cubic NES. Numerical studies reveal that the BNES is more effective in reducing vibration amplitude in the lock-in region. Like cubic NES, the inclusion of BNES de-stabilizes the large amplitude synchronized orbits in the lock-in region. The ability of BNES to exhibit inter-well chaotic motion is shown to cause larger vibration mitigation when compared with cubic NES. The transition from the intra-well periodic to inter-well chaotic motion is further investigated by Melnikov analysis, and the critical response amplitude needed for the same is arrived at. The complex-averaging (CX-A) method combined with the method of multiple scales (MMS) is used to derive the slow invariant manifold (SIM) from the slow-flow dynamics. The SIM topology, together with the projected time history, is used to demonstrate the advantages of BNES over cubic NES in vortex-induced vibration suppression. The effect of mass ratio, negative linear stiffness, non-dimensional damping, and stiffness ratio on the topology of SIM is investigated. Based on this parameter study, optimal BNES parameters for effective vibration suppression are suggested.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"150 ","pages":"Article 108952"},"PeriodicalIF":3.4,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168084","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":"QGCD algorithm for solving quaternion equation and its application in color image encryption","authors":"Manli Wang ,&nbsp;Caiqin Song ,&nbsp;V.I. Vasil’ev ,&nbsp;Gang Wang","doi":"10.1016/j.cnsns.2025.108943","DOIUrl":"10.1016/j.cnsns.2025.108943","url":null,"abstract":"<div><div>In this work, a new QGCD iterative algorithm is presented for finding the solution of a class of quaternion matrix equation. It is proved that if the studied quaternion matrix equation is consistent, the constructed algorithm can obtain the solution within finite iterative steps in the absence of round-off errors. Moreover, if the investigated quaternion matrix equation is inconsistent, the constructed algorithm can calculate the least squares solution within finite iterative steps in the absence of round-off errors for any (special) initial matrix. Moreover, a few of numerical examples are proposed to verify the effectiveness and superiority of the new algorithm and testify the conclusions suggested in this paper. Finally, the QGCD algorithm is applied to color image encryption, and the effectiveness of encryption is evaluated from four aspects, verifying the effectiveness of the encryption.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108943"},"PeriodicalIF":3.4,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125017","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 on mixed types of waves for an SIR epidemic model with infection–age structure and spatial diffusion","authors":"Xin Wu ,&nbsp;Rong Yuan ,&nbsp;Fangyuan Chen","doi":"10.1016/j.cnsns.2025.108928","DOIUrl":"10.1016/j.cnsns.2025.108928","url":null,"abstract":"<div><div>In Wu et al. (2021), Wu et al. studied an SIR epidemic model incorporating infection–age structure and spatial diffusion. It focused on the existence of traveling wave solutions when the diffusion coefficients met a technical condition (i.e., <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>≤</mo><mn>2</mn><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math></span>). Moreover, the question of the existence of traveling wave solutions with <span><math><mrow><mi>c</mi><mo>=</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span> remains open. This paper employs an approach rooted in the Schauder’s fixed-point theory, along with sophisticated upper and lower solution techniques, to show the existence of the super-critical and critical traveling wave solutions. Notably, it is established that the existence of this traveling wave solution is independent of the relative diffusivity ratio.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108928"},"PeriodicalIF":3.4,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125018","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":"Deflation-based certified greedy algorithm and adaptivity for bifurcating nonlinear PDEs","authors":"Federico Pichi ,&nbsp;Maria Strazzullo","doi":"10.1016/j.cnsns.2025.108941","DOIUrl":"10.1016/j.cnsns.2025.108941","url":null,"abstract":"<div><div>This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal decomposition have been widely investigated in the literature, but they usually rely on some <em>a-priori</em> knowledge about the bifurcating model and lack any error estimation. On the other hand, standard certified reduced basis techniques fail to represent correctly the branching behavior, since the error estimator is no longer reliable. The main goal of the contribution is to overcome these limitations by introducing two novel algorithms: (i) the adaptive-greedy, detecting the bifurcation point starting from scarce information over the parametric space, and (ii) the deflated-greedy, certifying multiple coexisting branches simultaneously. The former approach takes advantage of the features of the reduced manifold to detect the bifurcation, while the latter exploits the deflation and continuation methods to discover the bifurcating solutions and enrich the reduced space. We test the two strategies for the Coanda effect held by the Navier–Stokes equations in a sudden-expansion channel. The accuracy of the approach and the error certification are compared with vanilla-greedy and proper orthogonal decomposition.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108941"},"PeriodicalIF":3.4,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105821","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":"High-order mass- and energy-conserving methods for the coupled nonlinear Schrödinger equation","authors":"Pingrui Zhang ,&nbsp;Li Xia ,&nbsp;Hui Zhang ,&nbsp;Xiaoyun Jiang","doi":"10.1016/j.cnsns.2025.108944","DOIUrl":"10.1016/j.cnsns.2025.108944","url":null,"abstract":"<div><div>A novel high-order numerical method, specifically designed to preserve the mass and energy invariants of the coupled nonlinear Schrödinger equation (CNLS) is introduced. This algorithm integrates Gauss collocation schemes for temporal discretization with finite element methods for spatial discretization, enhanced by a post-processing correction procedure that ensures mass and energy conservation at each time step. The theoretical framework for the proposed method rigorously establishes the existence, uniqueness, and high-order convergence of the numerical solutions. In particular, the error of our proposed scheme is proven to converge at the rate of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>τ</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> in the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm, where <span><math><mi>τ</mi></math></span> and <span><math><mi>h</mi></math></span> denote the temporal and spatial step sizes, respectively, and <span><math><mi>k</mi></math></span> and <span><math><mi>p</mi></math></span> represent the degrees of the temporal and spatial finite element approximations, which can be arbitrarily high. The error analysis explicitly accounts for the cumulative effects of the post-processing correction across all time levels. A series of numerical experiments are presented to validate the proposed method, demonstrating its capacity to conserve mass and energy precisely, achieve high-order accuracy, and accurately capture soliton, bi-soliton and plane wave dynamics.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108944"},"PeriodicalIF":3.4,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115293","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":"DDoS attack on wireless cyber–physical systems: A Stackelberg game approach","authors":"Lianghong Peng,&nbsp;Youwen Yi,&nbsp;Zhijian Ji","doi":"10.1016/j.cnsns.2025.108945","DOIUrl":"10.1016/j.cnsns.2025.108945","url":null,"abstract":"<div><div>This paper delves into the network security issues of cyber–physical systems (CPSs), where malicious agents can launch distributed denial-of service (DDoS) attacks to disrupt communication channels between sensors and remote estimator. Addressing the strategic interaction between defenders and DDoS attacker, we establish a two-player zero-sum stochastic game framework that portrays the interaction as a dynamic Stackelberg non-cooperative game to deal with the impact of DDoS attacks on CPSs. Using refined Bayesian Nash equilibrium, we determine optimal attack-defense strategies and analyze scenarios with incomplete information. Notably, attacker can access sensor transmission power before acting, prompting us to propose solutions and optimal strategy algorithms. In simulations, we explore three transmission power ranges and thoroughly examine their impact on the utility functions of both attacker and defenders.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108945"},"PeriodicalIF":3.4,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105825","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":"An adaptive optimal selection approach of the Mixture-of-Experts model embedded with PINNs for one-dimensional hyperbolic conservation laws","authors":"Jiaqian Dan,&nbsp;Jiebao Sun,&nbsp;Jia Li,&nbsp;Shengzhu Shi","doi":"10.1016/j.cnsns.2025.108936","DOIUrl":"10.1016/j.cnsns.2025.108936","url":null,"abstract":"<div><div>In this paper, we propose a method of the mixture-of-experts (MoE) model embedded with physics-informed neural networks (PINNs) for the hyperbolic conservation laws. The issue on solving hyperbolic conservation laws with PINNs is still challenging since the solutions of conservation laws may contain discontinuities. PINNs, as functional approximators, nearly fail in such cases, and numerical solutions for its variants may suffer from various problems. Some specially designed variants of PINNs can be well applied to specific hyperbolic equations, but these models usually pay less attention to the generalization capability, and improvement can be made in computing efficiency. In view of this, we propose the adaptive algorithm that embeds PINNs with different strategies into the MoE model, which the algorithm selects “experts of PINNs” through a gating network, choosing the optimal strategy that every “expert” shows its expertise for different structures of the solution. We prove that the generalization error of the proposed model is not higher than that of any single expert, and the bounds for generalization error are also obtained. The numerical experiment results demonstrate the validity of our model and confirm the algorithm’s generalization capability that it is fully adaptable for different equations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108936"},"PeriodicalIF":3.4,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105113","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":"Mixed set-valued stochastic differential equations: Existence, uniqueness and averaging principle","authors":"Peiguang Wang ,&nbsp;Beibei Li ,&nbsp;Hairong Lian","doi":"10.1016/j.cnsns.2025.108935","DOIUrl":"10.1016/j.cnsns.2025.108935","url":null,"abstract":"<div><div>The objective of this paper is to investigate mixed set-valued stochastic differential equations with fractional Brownian motion, where the diffusion term is also set-valued. Under the non-Lipschitz continuity conditions, firstly, some new and reliable lemmas about the set-valued stochastic integral are provided. Secondly, we justify the existence and uniqueness of solutions to considered equations by successive approximations, stochastic analysis, and fractional calculus. Moreover, the solution converges to that of the averaged equations in the sense of mean square and probability. Finally, two examples are provided to verify our theoretical results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108935"},"PeriodicalIF":3.4,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105824","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":"Decentralized event-triggered reinforcement learning control for partially unknown nonlinear systems with time-varying states and asymmetric input constraints","authors":"Jingbo Zhong,&nbsp;Chunbin Qin,&nbsp;Yinliang Wu,&nbsp;Dehua Zhang,&nbsp;Tianzeng Zhu,&nbsp;Kaijun Jiang","doi":"10.1016/j.cnsns.2025.108937","DOIUrl":"10.1016/j.cnsns.2025.108937","url":null,"abstract":"<div><div>This paper proposes a decentralized event-triggered control scheme based on reinforcement learning to stabilize a class of partially unknown nonlinear mismatched interconnected systems with time-varying state constraints and asymmetric control input constraints. First, a meticulously designed barrier function, which combines traditional and smoothing functions, transforms a constrained interconnected system into an unconstrained one. To address the impact of mismatched interconnections, auxiliary systems are designed for each subsystem. Additionally, non-quadratic utility functions are employed to constrain the inputs of these auxiliary systems. By solving the optimal control scheme for the auxiliary systems, a decentralized control scheme for the integrated mismatched interconnected system is achieved. Unlike traditional actor–critic network structures, the proposed identifier–critic network structure relaxes the constraints on system dynamics and eliminates errors caused by approximating the actor-network. The weight vectors in the critic network are updated using gradient descent and concurrent learning techniques, eliminating the need for traditional persistent excitation conditions. Furthermore, an event-triggered mechanism is introduced to reduce computational load and communication overhead. According to Lyapunov stability theory, it is rigorously proven that all signals of the interconnected nonlinear system are bounded. Finally, simulation examples validate the effectiveness of the proposed control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"149 ","pages":"Article 108937"},"PeriodicalIF":3.4,"publicationDate":"2025-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144115161","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}