Multistability analysis of complex-valued recurrent neural networks with sine and cosine activation functions

This paper is devoted to the multistability problem for complex-valued recurrent neural networks (CVRNNs) with a specific class of piecewise nonlinear activation functions. Firstly, a general class of piecewise nonlinear activation functions is presented to facilitate further analysis. Then, by resorting to the fixed point theorem and Lagrange's mean value theorem, sufficient criteria are established which ascertain that the existence of (2k + 1)2" equilibrium points. Meanwhile, it also verifies that (k + 1)2" equilibrium points of the considered CVRNNs with a piecewise nonlinear activation function are stable, where k stands for a positive real number, which is associated with the frequency of sine and cosine functions. Moreover, the utilization of the activation functions provides a larger storage capacity in associative memory application. In the end of paper, three numerical examples are presented to demonstrate the feasibility and validity of the achieved theoretical results.