多时滞环形神经网络系统的与时滞相关和与时滞无关的稳定性分析  

Delay-dependent and Delay-independent Stability Analysis of a Ring Neural Network with Multiple Delays

作　　者：赵东霞[1] 王婷婷 范东霞 姚林红[1] ZHAO DONGXIA;WANG TINGTING;FAN DONGXIA;YAO LINHONG(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《应用数学学报》2022年第2期212-221,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金青年基金(61603351);山西省基础研究计划(20210302123046);山西省自然科学基金面上项目(201801D121027,201701D221121)资助。

摘　　要：本文对具有两个时滞的双向环形神经网络系统进行了稳定性分析.首先将系统在平凡解附近进行线性化处理,并得到线性化系统的特征方程,通过因式分解法,将系统的特征方程分解为四个一阶因子.其次,当系统参数在各种不同取值的情形下,通过构造辅助函数讨论了每个因子的零点均为负实部的条件,建立了与时滞相关及与时滞无关的稳定性结论.最后,本文还讨论了当环形神经网络中相邻两个神经元之间的连接被切断后所得的直线型神经网络系统的稳定性,在整个参数空间内全面地分析了系统稳定及不稳定的情况,得出了系统参数所满足的条件.数值仿真结果表明,直线型神经网络系统的参数取值范围更大,即更容易被镇定.In this paper,the stability of a bidirectional ring neural network system with two delays is analyzed.Firstly,the system is linearized around the trivial solution,and the characteristic equation of the linearized system is deduced.Then the characteristic polynomial of the system is decomposed into four first-order factors through the factorization method,hence,the characteristic values are equal to zeros of the four first-order factors.Secondly,by constructing auxiliary functions and discussing the different range of system parameters,we obtain the conditions that the zero of each factor has negative real part.Moreover,the delay-independent and delay-dependent stability results are established,and the allowable interval for delays are also given.Finally,we also study a linear neural network,which origins from the adjacent two neurons of the ring neural network is cut off.The stability and instability of the linear neural network are systematically discussed in the whole parameter space,and the range for system parameters are obtained.The numerical simulation results show that the linear neural network has a more wider range of parameters,that is,it is more easier to be stabilized than the ring architecture.

关 键 词：双向环形神经网络 多时滞 稳定性 

分 类 号：O175.13[理学—数学]