一类耦合logistics模型的动力学性质  

Dynamic Properties of a Coupled Logistic Model

作　　者：余江琼 刘娜 余志恒 YU Jiangqiong;LIU Na;YU Zhiheng(School of Mathematics,Southwest Jiaotong University,Chengdu 611756;School of General Education,Chengdu Industry and Trade College,Chengdu 611731,China)

机构地区：[1]西南交通大学数学学院,成都611756 [2]成都工贸职业技术学院通识教育学院,成都611731

出　　处：《重庆师范大学学报（自然科学版）》2023年第5期126-135,共10页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金青年科学基金项目(No.11701476);四川省自然科学基金面上项目(No.2023NSFSC0064)。

摘　　要：讨论一类离散捕食者-食饵模型的动力学性质,使用多项式完全判别系统和中心流形定理对该模型所对应的离散系统进行分析。由多项式完全判别系统给出了该模型不动点的拓扑分类,并找出了不动点在非双曲情形的参数条件;由中心流形定理证明了模型在不动点附近发生了transcritical分支和flip分支。运用数值模拟进一步验证了上述结果的正确性,并给出相应的Laypunov指数以说明模型在一定参数条件下产生了混沌现象。研究结果提示所讨论的模型在一定参数条件下可以产生transcritical分支、flip分支以及混沌等动力学性质。Discuss the dynamic properties of a class of discrete predator-prey models,and analyze the discrete system corresponding to the model by using polynomial complete discriminant system and central manifold theorem.The topological classification of the fixed points of the model was given by the polynomial complete discrimination system,and the parameter conditions for the fixed points in non-hyperbolic cases were found.By using central manifold theorem proves that the model undergoes transcritical and flip bifurcations near fixed points.The correctness of the above results was further verified through numerical simulation,and the corresponding Laypunov exponent was provided to demonstrate that the model produces chaotic phenomena under certain parameter conditions.The research results show that the model under discussion can generate dynamic properties such as transcritical bifurcatin,flip bifurcation,and chaos under certain parameter conditions.

关 键 词：耦合logistics模型 分支 多项式完全判别系统 中心流形 Laypunov指数 

分 类 号：O178[理学—数学]