单调激活函数惯性项神经耦合系统的混沌共存  

Chaos Coexistence of Inertial Neural System Based on a Monotonic Activation Function

作　　者：朱嘉奕 宋自根[1,2] ZHU Jiayi;SONG Zigen(College of Information,Shanghai Ocean University,Shanghai 201306,China;School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]上海海洋大学信息学院,上海201306 [2]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2023年第1期38-44,共7页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12172212);中央高校基本科研业务费专项资金资助(22120220588)。

摘　　要：混沌及其稳态共存是神经网络系统中一个重要研究热点问题.本文基于惯性项神经元模型,利用非线性单调激活函数构造了一个惯性项神经耦合系统,采用理论分析和数值模拟相结合的方法,研究了系统平衡点以及静态分岔的类型,分析了系统两种不同模式的混沌及其稳态共存.具体来说,我们通过选取不同的初始值,利用相应的相位图和时间历程图,展现了系统混沌对初值的敏感依赖性.进一步,采用耦合强度作为动力学的分岔参数,研究了混沌产生的倍周期分岔机制,得到了单调激活函数耦合下的惯性项神经元系统混沌共存现象.Chaos as well as its coexistence is an important research field in neural network systems.In this paper,based on a monotonic activation function,a neural network system is constructed by using inertial two-neuron model.By combining theoretical analysis and numerical simulation,the equilibrium point of the system and its static bifurcation style are studied.Specifically,two different modes of chaos and its steady-state coexistence are analyzed.In details,the sensitive dependence on initial values for chaos behavior is shown using the corresponding phase diagram and time history.Further,by employing the coupling strength as a bifurcation parameter,we present the period-doubling bifurcation of routes to chaos.The inertial neuronal system illustrates chaotic attractor coexistence.

关 键 词：惯性项神经元 单调激活函数 倍周期分岔 共存 混沌吸引子 

分 类 号：O175[理学—数学]