具有多时滞和多参数的双向环状网络的稳定性

Stability of the bidirectional ring networks with multiple time delays and multiple parameters

针对具有多时滞和多参数的四元双向环形神经网络系统进行动力学分析,首先在平凡解附近对系统进行线性化处理,得到系统的特征方程。然后对特征方程进行因式分解,将其分解为四个一阶指数型多项式的连乘。进而,利用指数型多项式零点分布性质,建立系统与时滞相关及与时滞无关的稳定性充分条件。此外,将所得结论与已有文献中的结果做了详尽的对比分析,并利用数值模拟佐证了理论分析的有效性和优越性。

The dynamic analysis of the four-neuron ring neural network with multiple time delays and multiple parameters is carried out.Firstly,the system is linearized near the trivial solution,and the characteristic equation of the system is obtained.Then the characteristic equation is factorized into four first-order exponential polynomials.Furthermore,by using the zero-point distribution property of exponential polynomial,sufficient conditions for the delay-dependent and delay-independent stability are established.Moreover,an exhaustive comparison analysis is made between the results obtained and those in the existing literature.Finally,some numerical simulations are presented to show the effectiveness and superiority of the results.