Stability and Hopf bifurcation of a neural network model with distributed delays and strong kernel

Abstract

In this paper, the dynamical behaviors of a two-neuron network model with distributed delays and strong kernel are investigated. Considering the mean delay as a bifurcation parameter, explicit algorithms for determining the conditions of Hopf bifurcation are derived. A family of periodic solutions bifurcate from an equilibrium when the bifurcation parameter exceeds a critical value. The direction and stability of the bifurcating periodic solutions are determined in detail by using the theory of normal form and center manifold.Numerical simulations are performed to illustrate the effectiveness of the results found.

On the global attractivity of non-autonomous neural networks with a distributed delay

“…For scalar equations with a distributed delay, stability, either dependent or independent of the delay distribution, has been studied by several authors [5,6,8,15,35]. A particular case of a system of two equations was explored in [7,16].…”

On the global attractivity of non-autonomous neural networks with a distributed delay

“…For scalar equations with a distributed delay, stability, either dependent or independent of the delay distribution, has been studied by several authors [5,6,8,15,33]. A particular case of a system of two equations was explored in [7,16].…”