Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"Modified hat functions for constrained fractional optimal control problems with ψ-Caputo derivative","authors":"Sh. Karami ,&nbsp;M.H. Heydari ,&nbsp;D. Baleanu ,&nbsp;M. Bayram","doi":"10.1016/j.cnsns.2025.108657","DOIUrl":"10.1016/j.cnsns.2025.108657","url":null,"abstract":"<div><div>In this paper, a class of constrained fractional optimization problems under a dynamic system involving the <span><math><mi>ψ</mi></math></span>-Caputo fractional derivative is introduced. A computational method based on the modified hat basis functions is developed to solve these problems. This work is done by obtaining a new operational matrix for the <span><math><mi>ψ</mi></math></span>-Riemann–Liouville fractional integral of the modified hat functions. The established approach utilizes the modified hat functions to approximate the state and control variables, successfully converting the main problem into a set of algebraic equations. This method provides a systematic and efficient way to obtain numerical solutions for this class of problems. Several test problems are examined to verify the accuracy and applicability of the proposed method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108657"},"PeriodicalIF":3.4,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349553","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":"Regularity and strong convergence of numerical approximations for stochastic wave equations with multiplicative fractional Brownian motions","authors":"Dehua Wang ,&nbsp;Xiao-Li Ding ,&nbsp;Lili Zhang ,&nbsp;Xiaozhou Feng","doi":"10.1016/j.cnsns.2025.108648","DOIUrl":"10.1016/j.cnsns.2025.108648","url":null,"abstract":"<div><div>Stochastic wave equations with multiplicative fractional Brownian motions (fBms) provide a competitive means to describe wave propagation process driven by inner fractional noise. However, regularity theory and approximate solutions of such equations is still an unsolved problem until now. In this paper, we achieve some progress on the regularity and strong convergence of numerical approximations for a class of semilinear stochastic wave equations with multiplicative fBms. Firstly, we impose some suitable assumptions on the nonlinear term multiplied by fBms and its Malliavin derivatives, and analyze the temporal and spatial regularity of stochastic convolution operator under the assumptions for two cases <span><math><mrow><mi>H</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>H</mi><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. Using the obtained regularity results of the stochastic convolution operator, we further establish the regularity theory of mild solution of the equation, and reveal quantitatively the influence of Hurst parameter on the regularity of the mild solution. Besides that, we give a fully discrete scheme for the stochastic wave equation and analyze its strong convergence. Finally, two numerical examples are carried out to verify the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108648"},"PeriodicalIF":3.4,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349360","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":"Finite-time contractive stabilization for fractional-order switched systems via event-triggered impulse control","authors":"P. Gokul ,&nbsp;Ardak Kashkynbayev ,&nbsp;M. Prakash ,&nbsp;Rakkiyappan Rajan","doi":"10.1016/j.cnsns.2025.108658","DOIUrl":"10.1016/j.cnsns.2025.108658","url":null,"abstract":"<div><div>This article investigates the issue of finite-time stabilization for fractional-order switched nonlinear system (FOSNS) under the novel framework of mode-dependent event-triggered mechanism (MDETM). Initially, this study effectively addresses Zeno behavior (ZB) avoidance in FOSNS by the MDETM approach. This mechanism operates through the strategy of event-triggered impulsive control (ETIC) and the constraint of mode-specific average dwell time. Following this, we establish finite-time stability (FTS) and finite-time contractive stability (FTCS) for general FOSNS by employing the Lyapunov-based methodology. This approach is employed to analyze situations where the fractional derivatives of Lyapunov functions (LFs) of the modes are indefinite. Furthermore, the criteria of ZB, FTS, and FTCS are validated for application of FOSNS that adheres to the same framework as proposed for general FOSNS. The utilization of linear matrix inequality (LMI) was employed to derive the control gain matrix, ensuring the preservation of the stability property. To conclude, the efficacy of the introduced ETIC strategies is demonstrated through the analysis of two illustrative examples.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108658"},"PeriodicalIF":3.4,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349500","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":"Two lower boundedness-preservity auxiliary variable methods for a phase-field model of 3D narrow volume reconstruction","authors":"Xiangjie Kong,&nbsp;Renjun Gao,&nbsp;Boyi Fu,&nbsp;Dongting Cai,&nbsp;Junxiang Yang","doi":"10.1016/j.cnsns.2025.108649","DOIUrl":"10.1016/j.cnsns.2025.108649","url":null,"abstract":"<div><div>Three-dimensional (3D) volume reconstruction remains a fundamental technique with wide applications in fields such as 3D printing, medical diagnostics, and industrial design. This paper presents two novel lower boundedness-preserving auxiliary variable methods designed for the phase-field model of 3D narrow volume reconstruction. By employing scattered point data, our approach reconstructs smooth narrow volumes using a phase-field Allen–Cahn model with a control function. The proposed method ensures energy dissipation and smooth surface throughout the reconstruction process. By introducing an auxiliary variable, the nonlinear term in the governing equation is reformulated, allowing for efficient time-marching schemes. The fully discrete scheme is linear, and its unconditional stability is rigorously estimated. Numerical experiments are conducted to demonstrate the energy stability, accuracy, and effectiveness of our proposed methods in various 3D reconstruction tasks, establishing its broad applicability.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108649"},"PeriodicalIF":3.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349933","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":"Traveling waves in a generalized Bogoyavlenskii coupled system under perturbation of distributed delay and weak dissipation","authors":"Feiting Fan ,&nbsp;Xingwu Chen","doi":"10.1016/j.cnsns.2025.108647","DOIUrl":"10.1016/j.cnsns.2025.108647","url":null,"abstract":"<div><div>In this paper, we focus on the traveling waves for a perturbed generalized Bogoyavlenskii coupled system with delay convection term and weak dissipation, including periodic waves, solitary waves, kink and anti-kink waves. The corresponding traveling wave equation can be transformed into a 4-dimensional dynamical system, which is regarded as a singularly perturbed system and is reduced to a near-Hamiltonian form. We construct a locally invariant manifold diffeomorphic to the critical manifold with normally hyperbolicity and then give the existence conditions of traveling waves by the geometric singular perturbation theory as well as the number of periodic waves by analyzing the monotonicity of ratios of Abelian integrals. Moreover, the monotonicity of the wave speed is provided as well as its supremum and infimum. Numerical simulations are in complete agreement with the theoretical predictions.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108647"},"PeriodicalIF":3.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349503","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":"Crossing limit cycles in piecewise smooth Kolmogorov systems: An application to Palomba’s model","authors":"Yagor Romano Carvalho ,&nbsp;Luiz F.S. Gouveia ,&nbsp;Oleg Makarenkov","doi":"10.1016/j.cnsns.2025.108646","DOIUrl":"10.1016/j.cnsns.2025.108646","url":null,"abstract":"<div><div>In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones separated by a straight line. In particular, we study the number of crossing limit cycles of small amplitude. They are all nested and surround one equilibrium point or a sliding segment. We denote by <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> the maximum number of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov systems of degree <span><math><mrow><mi>n</mi><mo>=</mo><mi>m</mi><mo>+</mo><mn>1</mn></mrow></math></span>. We make a progress towards the determination of the lower bounds <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>K</mi></mrow><mrow><mi>p</mi></mrow></msubsup><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> of crossing limit cycles bifurcating from the equilibrium point via a degenerate Hopf bifurcation for a piecewise smooth Kolmogorov system of degree <span><math><mi>n</mi></math></span>. Specifically, we shot that <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>≥</mo><mn>12</mn></mrow></math></span>, and <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow><mrow><mi>c</mi></mrow></msubsup><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mo>≥</mo><mn>18</mn></mrow></math></span>. In particular, we show at least one crossing limit cycle in Palomba’s economics model, considering it from a piecewise smooth point of view. To our knowledge, these are the best quotes of limit cycles for piecewise smooth polynomial Kolmogorov systems in the literature.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108646"},"PeriodicalIF":3.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349934","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":"Exponential stability estimate for derivative nonlinear Schrödinger equation","authors":"Xue Yang","doi":"10.1016/j.cnsns.2025.108644","DOIUrl":"10.1016/j.cnsns.2025.108644","url":null,"abstract":"<div><div>We consider the derivative nonlinear Schrödinger equations <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub><mo>+</mo><mi>V</mi><mo>∗</mo><mi>u</mi><mo>+</mo><mi>i</mi><msub><mrow><mi>∂</mi></mrow><mrow><mi>x</mi></mrow></msub><mfenced><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mover><mrow><mi>u</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow></msub><mi>F</mi><mfenced><mrow><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow></mfenced></mrow></mfenced><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><mi>T</mi></mrow></math></span></span></span>with a nonlinearity <span><math><mrow><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mover><mrow><mi>u</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span> of order at least <span><math><mn>3</mn></math></span> at the origin. We prove that for almost all <span><math><mi>V</mi></math></span>, if the initial data is <span><math><mi>ɛ</mi></math></span>-small in the modified Sobolev space, the solution is stable over time intervals of order <span><math><mrow><msup><mrow><mi>ɛ</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ɛ</mi></mrow></mfrac></mrow></msup><mi>⋅</mi><msup><mrow><mi>e</mi></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ɛ</mi></mrow></mfrac></mrow></msup></mrow></msup></mrow></math></span>. Our findings extend the stability time <span><math><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><mfenced><mrow><mo>ln</mo><mi>ɛ</mi></mrow></mfenced></mrow><mrow><mi>ɛ</mi></mrow></mfrac></mrow></msup></math></span> introduced by Cong (2022) to <span><math><msup><mrow><mi>e</mi></mrow><mrow><msup><mrow><mi>e</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ɛ</mi></mrow></mfrac></mrow></msup></mrow></msup></math></span>.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108644"},"PeriodicalIF":3.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183434","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":"Limit cycle bifurcations in a class of piecewise Hamiltonian systems","authors":"Wenwen Hou,&nbsp;Maoan Han","doi":"10.1016/j.cnsns.2025.108643","DOIUrl":"10.1016/j.cnsns.2025.108643","url":null,"abstract":"<div><div>In this paper, we first obtain explicit expressions of up to fourth order Melnikov functions for a class of piecewise Hamiltonian systems with two zones separated by two semi-straight lines. Then based on these expressions, we give upper bounds of the number of limit cycles bifurcated from a period annulus of a piecewise linear system under piecewise polynomial perturbations. The upper bounds are sharp for some cases of lower degrees.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108643"},"PeriodicalIF":3.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183736","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":"The Cauchy matrix structure and solutions of the three-component mKdV equations","authors":"Mengli Tian ,&nbsp;Chunxia Li ,&nbsp;Yehui Huang ,&nbsp;Yuqin Yao","doi":"10.1016/j.cnsns.2024.108456","DOIUrl":"10.1016/j.cnsns.2024.108456","url":null,"abstract":"<div><div>Starting from a 4 × 4 matrix Sylvester equation, the matrix mKdV system as an unreduced equation is worked out and the explicit expression of its solution is presented by applying the Cauchy matrix method. Then, two kinds of reduction conditions are given, under which the complex three-component mKdV(CTC-mKdV) equation and the real three-component mKdV(RTC-mKdV) equation can be obtained, and finally, the explicit expressions of soliton solution and Jordan block solution for CTC-mKdV equation and RTC-mKdV equation are presented, respectively. Specially, the generated conditions of one-soliton solutions, two-soliton solutions, double-pole solutions, symmetry broken solutions and soliton molecule are presented, and their dynamic behaviors were analyzed.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"141 ","pages":"Article 108456"},"PeriodicalIF":3.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180286","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":"Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method","authors":"Bertin Many Manda ,&nbsp;Malcolm Hillebrand ,&nbsp;Charalampos Skokos","doi":"10.1016/j.cnsns.2025.108635","DOIUrl":"10.1016/j.cnsns.2025.108635","url":null,"abstract":"<div><div>We present a method for the computation of the Generalized Alignment Index (GALI), a fast and effective chaos indicator, using a multi-particle approach that avoids variational equations. We show that this approach is robust and accurate by deriving a leading-order error estimation for both the variational (VM) and the multi-particle (MPM) methods, which we validate by performing extensive numerical simulations on two prototypical models: the two degrees of freedom Hénon-Heiles system and the multidimensional <span><math><mi>β</mi></math></span>-Fermi-Pasta–Ulam-Tsingou chain of oscillators. The dependence of the accuracy of the GALI on control parameters such as the renormalization time, the integration time step and the deviation vector size is studied in detail. We test the MPM implemented with double precision accuracy (<span><math><mrow><mi>ɛ</mi><mo>≈</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>16</mn></mrow></msup></mrow></math></span>) and find that it performs reliably for deviation vector sizes <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≈</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>, renormalization times <span><math><mrow><mi>τ</mi><mo>≲</mo><mn>1</mn></mrow></math></span>, and relative energy errors <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>≲</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>. These results hold for systems with many degrees of freedom and demonstrate that the MPM is a robust and efficient method for studying the chaotic dynamics of Hamiltonian systems. Our work makes it possible to explore chaotic dynamics with the GALI in a vast number of systems by eliminating the need for variational equations.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108635"},"PeriodicalIF":3.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143257792","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}