Stability and Hopf-bifurcation analysis of four dimensional minimal neural network model with multiple time delays

Abstract

In this paper, a minimal neural networks (NNs) of four dimensional (4D) model is considered with two different and discrete time delays. The time delay in information transformation follows the finite propagation speed of the signals and the finite processing time in the synapses. The linear stability and the local Hopf-bifurcation of the model are investigated by analyzing the associated characteristic equation. Stability of bifurcating periodic solutions and direction of the Hopf-bifurcation are determined using the normal form theory and center manifold theorem. Numerical simulations are performed to justify the theoretical results. Finally, the bifurcation diagrams are performed to observe the dynamical characteristics of the neuron model. Therefore, these results could be useful to understand the contribution of multiple time delays in excitable neural systems for signal processing.