单调激活函数惯性项神经耦合系统的混沌共存

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 Coexistence of Inertial Neural System Based on a Monotonic Activation Function

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.