Stability and Hopf Bifurcation of Multi-ring Coupling Neural Network with Delays

Most previous studies with respect to bifurcation dynamics of neural networks are limited to low dimensional or simple single ring structure. It should be noted that neural networks are composed of thousands of neurons, and these network structures are so complex that cannot be accurate representation by a single ring structure or several nodes. Therefore, it has greater practicality and the potential to study the model of high-dimensional or multi-ring coupling neural network. However, how to obtain characteristic equations of high dimensional systems is an unavoidable problem for researchers. In current paper, a model with four rings coupling neural network is proposed, and the stability and Hopf bifurcation of this model arc studied. In order to overcome the obstacle of solving characteristic equation by higher order determinant, the Coates slow graph method is used to obtain the characteristic equations of higher order neural network model. Finally, some numerical simulation examples are given to demonstrate the validity of proposed theoretical results, meanwhile the relation between the number of rings and bifurcation point is given by simulation.