Multistability

Physics

Nonlinear system

Recurrent neural network

Computer science

Quantum mechanics

Pattern recognition (psychology)

Instability

Mechanics

Control theory (sociology)

Artificial neural network

Control (management)

Artificial intelligence

Neural Networks

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 [Formula: see text] equilibria, [Formula: see text] 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.

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