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

Hadadi, Javad; ‎Khoshsiar Ghaziani, Reza; Alidousti, Javad; Eskandari, Zohreh

doi:10.22124/jmm.2024.26038.2309

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

10.22124/jmm.2024.26038.2309

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.

Keywords