Global stability and Hopf bifurcation of delayed fractional-order complex-valued BAM neural network with an arbitrary number of neurons

Document Type : Research Article


1 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran


In this paper, a general class of fractional-order complex-valued bidirectional associative memory neural network with time delay is considered. This neural network model contains an arbitrary number of neurons, i.e. one neuron in the X-layer and other neurons in the Y-layer. Hopf bifurcation analysis of this system will be discussed. Here, the number of neurons, i.e., $n$ can be chosen arbitrarily. We study Hopf bifurcation by taking the time delay as the bifurcation parameter. The critical value of the time delay for the occurrence of Hopf bifurcation is determined. Moreover, we find two kinds of appropriate Lyapunov functions that under some sufficient conditions, global stability of the system is obtained. Finally, numerical examples are also presented.