Multistability and instability analysis of recurrent neural networks with time-varying delays

This paper provides new theoretical results on the multistability and instability analysis of recurrent neural networks with time-varying delays. It is shown that such n-neuronal recurrent neural networks have exactly (4k+3)k0 equilibria, (2k+2)k0 of which are locally exponentially stable and the others are unstable, where k0 is a nonnegative integer such that k0≤n. By using the combination method of two different divisions, recurrent neural networks can possess more dynamic properties. This method improves and extends the existing results in the literature. Finally, one numerical example is provided to show the superiority and effectiveness of the presented results.