The stability and Hopf bifurcation analysis for the delay diffusive neural networks model

Abstract

In this paper the semi-analytical solution is investigated for the delayed diffusive neural network model. Delay partial differential equations are approximated to the delay ordinary differential equation systems, by using Galerkin technique method. The main aim of this work is to determine the effect of diffusion and delay parameters and exploring the full map of stability analysis of the system. Stability analysis and bifurcation maps are discussed, as well, and in order to further explain certain concepts. The effect of diffusion parameter and delay values is comprehensively studied and as a result both variables can destabilize or stabilize the system. Illustrated examples of the unstable and stable limit cycles, and the Hopf bifurcation points are shown to prove the formerly revealed outcomes in the Hopf bifurcation map. In addition, comparisons between the numerical results and semi-analytical outcome provide comparison for all figures shown in the work.