A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

Abstract

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.

Keywords:

• BAM neural networks
• time-varying delays
• reaction-diffusion
• exponential stability
• graph theory

AMS Subject Classifications:

• 94C15
• 34D20

Acknowledgements

The authors really appreciate the reviewers’ valuable comments.

Notes

This work was supported by the NNSF of China [grant number 11301115], [grant number 11301112], [grant number 11271101], [grant number 51208150]; the NSF of Shandong Province [grant number ZR2013AQ003].