Bifurcation analysis in a discrete BAM network model with delays

^†This research is supported by the National Natural Science Foundation of China (No.10771045) and Program of Excellent Team in Harbin Institute of Technology.

Abstract

In this paper, a discrete bidirectional associative memory network model consisting of three neurons is considered. We study the stability of the equilibria of the system by analysing the distribution of the eigenvalues. It is found that there are three kinds of bifurcations: Pitchfork bifurcation, Period-Doubling bifurcation and Neimark–Sacker bifurcation. The direction and stability of the Neimark–Sacker are determined by using normal forms and centre manifold theory. Some numerical simulations are carried out to illustrate the analytical results.

Keywords:

• discrete neural network
• delay
• Neimark–Sacker bifurcation
• stability

Acknowledgements

We wish to thank the reviewers and Professor Elaydi for their valuable comments and suggestions that led to truly significant improvement of the manuscript.

Notes

^†This research is supported by the National Natural Science Foundation of China (No.10771045) and Program of Excellent Team in Harbin Institute of Technology.