Multistability of complex-valued recurrent neural networks with real-imaginary-type activation functions

This paper addresses the multistability problem of n-dimensional complex-valued recurrent neural networks with real-imaginary-type activation functions. Sufficient conditions are proposed for checking the existence of [(2α+1)(2β+1)]n (α,β⩾1) equilibria. Under these conditions, [(α+1)(β+1)]n equilibria are locally exponentially stable and the others are unstable. Attractive basins of equilibria are also investigated. Complete attractive basins of equilibria in 1-dimensional complex-valued recurrent neural networks are obtained. The obtained stability results improve and extend the existing ones. Two numerical examples are given to illustrate the effectiveness of the obtained results.