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In this brief, stability of multiple equilibria of recurrent neural networks with time-varying delays and the piecewise linear activation function is studied. A sufficient condition is obtained to ensure that n-neuron recurrent neural networks can have (4k - 1)(n) equilibrium points and (2k)(n) of them are locally exponentially stable. This condition improves and extends the existing stability results in the literature. Simulation results are also discussed in one illustrative example.

In this paper, the multiperiodicity of a general class of discrete-time delayed neural networks (DTDNNs) is formulated and studied. Several sufficient conditions are obtained to ensure n-neuron DTDNNs can have 2n periodic orbits and these periodic orbits are locally attractive. In addition, we give the conditions for a periodic orbit to be locally or globally attractive when the periodic orbit locates in a designated region. As two typical representatives, the Hopfield neural network and the cellular neural network are examined in detail. These conditions improve and extend the existing stability results in the literature. Simulations results are also discussed in three illustrative examples.

This paper presents new theoretical results on global exponential stability of recurrent neural networks with bounded activation functions and time-varying delays. The stability conditions depend on external inputs, connection weights, and time delays of recurrent neural networks. Using these results, the global exponential stability of recurrent neural networks can be derived, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail.