Multistability of Complex-Valued NNs With General Periodic-Type Activation Functions and Its Application to Associative Memories

This article mainly studies the multistability of complex-valued neural networks (CVNNs) with general periodic-type activation functions. In order to improve the storage capacity of associative memory, a general periodic-type activation function is introduced which obtains three different numbers of equilibrium points (EPs), including unique, finite, and countable infinite. The existence and stability of equilibria are investigated based on Brouwer’s fixed point theorem and ${M}$ -matrix method. By means of a sign function on complex numbers, stability is confirmed using a new norm on the absolute values of the real and imaginary parts. The attraction basins of exponentially stable equilibria are estimated, which are bigger than the subspaces of the original division. Also, the design of associative memory is given. Finally, two numerical simulation examples verify the obtained results.