时滞耦合惯性项神经系统的多混沌路径共存  

Multistage Coexistence of Different Chaotic Routes in a Delayed Neural System

作　　者：李小虎 张定一 宋自根[1] LI Xiaohu;ZHANG Dingyi;SONG Zigen(College of Information Technology,Shanghai Ocean University,Shanghai 201306,P.R.China;College of Food Sciences and Technology,Shanghai Ocean University,Shanghai 201306,P.R.China)

机构地区：[1]上海海洋大学信息学院,上海201306 [2]上海海洋大学食品学院,上海201306

出　　处：《应用数学和力学》2020年第6期636-645,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11672177)。

摘　　要：混沌及其共存是神经动力学的一个重要研究内容.该文基于非单调激活函数的惯性项神经元时滞耦合系统,在固定系统参数的情况下,以耦合时滞τ作为参变量,取不同的初始条件,利用Poincaré截面技术,展现了系统多个不同的倍周期分岔序列和概周期分岔序列,并给出了系统相应的相图.研究结果表明,时滞耦合神经系统具有多级倍周期分岔序列和概周期分岔序列的稳态共存,展现了系统更加丰富的多混沌和多周期解的多稳态共存.Chaos and its coexistence involve very important problems in dynamical analysis.A delayed inertial 2⁃neuron system with non⁃monotonic activation function was studied with the Poincarésection method.With system parameters fixed and time delayτchosen as the paramet⁃ric variable,1D bifurcation diagrams,i.e.period⁃doubling and quasi⁃periodic bifurcations were given under different initial conditions.The results show that,the neural system exhibits multi⁃stage coexistence of many period⁃doubling and quasi⁃periodic bifurcation sequences along dif⁃ferent routes to chaos and stable coexistence of many chaotic attractors and multi⁃periodic solu⁃tions.

关 键 词：神经系统 时滞 倍周期分岔 概周期分岔 共存 混沌路径 

分 类 号：O175[理学—数学]