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 asparameter

the stability of the system is investigated Firstly

the resultingsystem with one delay is analyzed By analyzing its associated characteristicequation

local stability and the existence of Hopf bifurcation of the systemare investigated Secondly

the resulting system with three delays is analyzedIt is found that the delays can lead the system dynamic behavior to exhibitstability switches

and Hopf bifurcation occurs when the delay crosses somecritical value Finally

numerical simulations are given to illustrate theobtained results and numerical simulations also show that in the system thereexist the synchronous (asynchronous) periodic oscillations