广义(2+1)维Hirota-Maccari系统的动力学及混沌行为  

Dynamics and Chaotic Behavior of Generalized(2+1)-Dimensional Hirota-Maccari System

作　　者：张冬梅 梁建莉[1] ZHANG Dongmei;LIANG Jianli(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报(自然科学版)》2025年第1期113-120,共8页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金青年基金资助项目(11901215);福建省自然科学基金资助项目(2022J01303)。

摘　　要：采用微分方程定性理论和动力系统分支方法研究广义(2+1)维Hirota-Maccari系统的动力学及混沌行为,获得对应行波系统的分支相图,得到系统的周期波解和孤立波解的精确表达式。通过数值模拟研究不同参数条件下的行波解波形及其性质的变化,对该系统增加一个周期扰动项之后,利用Matlab软件得到扰动系统在一些特殊参数条件下的2D相图、3D相图和庞加莱截面。结果表明:该系统在特定参数条件下的运动是准周期的。The dynamics and chaotic behavior of generalized(2+1)-dimensional Hirota-Maccari system are studied by the qualitative theory of differential equations and the bifurcation method of dynamical systems,the bifurcations of phase portraits of the corresponding traveling wave system are obtained,and the exact expressions of the periodic wave solutions and solitary wave solutions of the system are obtained.Numerical simulation is carried out to study the wave forms and properties of traveling wave solutions under different parameter conditions.After adding periodic perturbation term to the system,2D phase portrait,3D phase portrait and Poincare section of the perturbed system are obtained by Matlab software under the special parameter conditions.The results show that the motion of the system is quasi-periodic under specific parameter conditions.

关 键 词：广义(2+1)维Hirota-Maccari系统 行波解 孤立波解 混沌行为 

分 类 号：O175.29[理学—数学]