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

Publish Year: 1402
Type: Journal paper
Language: English
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JR_JMMO-11-1_002

Index date: 8 June 2024

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

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.

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

Neural Network , fractional ordinary differential equations , Hopf bifurcation , time delay , Lyapunov function

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

Elham Javidmanesh

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

Alireza Zamani Bahahbadi

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