Communications in Nonlinear Science and Numerical Simulation最新文献

{"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}

{"title":"Qualitative theoretical research on solutions of fractional switched systems with variable-time switching mechanism","authors":"Zeming Zhao ,&nbsp;Yunfei Peng","doi":"10.1016/j.cnsns.2025.108645","DOIUrl":"10.1016/j.cnsns.2025.108645","url":null,"abstract":"<div><div>This paper is devoted to the qualitative theory of a class of fractional switched systems with a variable-time switching mechanism (FSSVT). FSSVT is a new class of state-feedback fractional switched systems, where the active regions of each subsystem vary with time. Initially, we obtain the condition of the existence and uniqueness of the global solution for FSSVT and give a criterion for determining the number of switching. Subsequently, by introducing a topology constructed from the approximate solutions of FSSVT, we obtain the continuous dependence and Gâteaux differentiability of solutions with respect to initial values in a weak sense. Finally, we investigate the periodicity of solutions for FSSVT and provide an example.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108645"},"PeriodicalIF":3.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143349552","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":"Practical fixed-time consensus for continuous action iterated dilemmas under communication and learning constraints","authors":"Hasnain Ali ,&nbsp;Syed Muhammad Amrr","doi":"10.1016/j.cnsns.2025.108642","DOIUrl":"10.1016/j.cnsns.2025.108642","url":null,"abstract":"<div><div>This paper introduces a continuous action iterated dilemma (CAID) model, enabling agents to adopt a spectrum of strategies beyond the traditional game theory practice of having only binary options. Existing research on the CAID problem often overlooks real-world challenges and assumes perfect communication and learning rates among agents. This work considers the limitations of complex networks, such as communication delays, restricted learning rates of agents, dynamic uncertainty, and information losses during data transmission. The proposed strategy employs a fixed-time convergent algorithm with Artstein transformation that transforms a delay-induced system into a delay-free model, and the fixed-time design ensures consensus among all agents within a fixed and bounded timeframe, regardless of the initial conditions. The convergence analysis of the proposed CAID strategy is conducted using Lyapunov theory, validating the practical fixed-time convergence of consensus despite communication delays, confined learning rates, model uncertainty, and information loss. Numerical simulations under varying conditions demonstrate that the proposed approach facilitates faster consensus attainment and requires fewer iterations than the existing method.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108642"},"PeriodicalIF":3.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143183735","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":"Data-driven optimal prediction with control","authors":"Aleksandr Katrutsa ,&nbsp;Ivan Oseledets ,&nbsp;Sergey Utyuzhnikov","doi":"10.1016/j.cnsns.2025.108641","DOIUrl":"10.1016/j.cnsns.2025.108641","url":null,"abstract":"<div><div>This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved variables. The latter variables cannot be measured explicitly. They may have smaller amplitudes and affect the resolved variables that can be measured. The optimal prediction approach recovers the averaged trajectories of the resolved variables by computing conditional expectations, while the distribution of the unresolved variables is assumed to be known. We consider such dynamical systems and introduce their additional control functions. To predict the targeted trajectories numerically, we develop a data-driven method based on the dynamic mode decomposition. The proposed approach takes the <em>measured</em> trajectories of the resolved variables, constructs an approximate linear operator from the Mori–Zwanzig decomposition, and reconstructs the <em>averaged</em> trajectories of the same variables. It is demonstrated that the method is much faster than the Monte Carlo simulations and it provides a reliable prediction. We experimentally confirm the efficacy of the proposed method for two Hamiltonian dynamical systems.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"143 ","pages":"Article 108641"},"PeriodicalIF":3.4,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143057358","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}