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 ( 2 α + 1 ) ( 2 β + 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.