Dynamics and bifurcations of a discrete-time neural network model with a single delay

Document Type : Research Article

Authors

1 Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran

2 Department of Mathematical Sciences‎, ‎Shahrekord University‎, ‎Shahrekord‎, ‎Iran

3 Department of Mathematics, Faculty of Science, Fasa University, Fasa, Iran

Abstract

In the present study, we analyze dynamics and bifurcations of a discrete-time    Hopfield neural network  based on two neurons and the same time delay. We determine stability and bifurcations of the system consisting flip, pitchfork and Neimark-Sacker  bifurcations. The normal form coefficients for the all bifurcations are calculated using reducing to the corresponding  center manifold, then these coefficients are  numerically obtained using MatContM. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.

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Journal of Mathematical Modeling
Volume 12, Issue 3
September 2024
Pages 419-430

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