一类多时滞细胞神经网络系统的稳定性转换  

Stability Switches in a Cellular Neural Network with Multiple Delays

作　　者：张婷婷[1] 马淑芳[1] ZHANG Ting-ting;MA Shu-fang(Department of Mathematic,Northeast Forestry University,Harbin 150000,China)

机构地区：[1]东北林业大学数学系,哈尔滨150000

出　　处：《哈尔滨理工大学学报》2019年第6期147-154,共8页Journal of Harbin University of Science and Technology

基　　金：中央高校基本科研业务费专项资金资助项目(2572018BC19).

摘　　要：为了分析时滞变化对细胞神经网络系统稳定性的影响,研究了一类具有三个时滞的细胞神经网络系统。以时滞作为参数,研究了该系统的稳定性。首先考虑了单时滞的情形。通过讨论相关的特征方程特征根的分布,分析了了系统的局部稳定性及Hopf分支的存在性。其次,考虑多时滞情形。发现当时滞穿过一系列临界值时,时滞会导致系统显示稳定性转换现象和产生Hopf分支。最后,通过数值算例验证了所得结果。数值模拟显示系统也存在同步(异步)周期振动现象。In order to analyze the effect of time-delay on the stability of the cellular neural network,a cellular neural network with three delays is considered.Considering delay as parameter,the stability of the system is investigated.Firstly,the resulting system with one delay is analyzed.By analyzing its associated characteristic equation,local stability and the existence of Hopf bifurcation of the system are investigated.Secondly,the resulting system with three delays is analyzed.It is found that the delays can lead the system dynamic behavior to exhibit stability switches,and Hopf bifurcation occurs when the delay crosses some critical value.Finally,numerical simulations are given to illustrate the obtained results and numerical simulations also show that in the system there exist the synchronous(asynchronous)periodic oscillations.

关 键 词：细胞神经网络 时滞 渐近稳定 HOPF分支 稳定性转换 

分 类 号：O175[理学—数学]