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

摘要

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.