Stability and Hopf bifurcation analysis of a simplified six-neuron tridiagonal two-layer neural network model with delays

Abstract

Firstly, a general tridiagonal two-layer neural network model with 2n-neuron is proposed, where every layer has time delay. A new method of Hopf bifurcation analysis is introduced by matrix decomposition in this paper. Through factoring the tridiagonal matrix, the characteristic equation of the neural network model is simplified. Secondly, by studying the eigenvalue equations of the related linear system for the special six-neuron (three neurons per layer) two-layer neural network model, the sufficient conditions for experiencing the Hopf bifurcation are obtained. The conditions obtained by the new method proposed in this paper are simpler and more practical than those obtained by the traditional Hurwitz discriminant method. Next, based on the normal form method and the center manifold theorem, the explicit formulae about the stability of the bifurcating periodic solution and the direction of the Hopf bifurcation are established. Finally, the main results obtained in this paper are illustrated by three numerical simulation examples.