Multistability in Mittag-Leffler sense of fractional-order neural networks with piecewise constant arguments

Abstract

Abstract This paper discusses the multistability in Mittag-Leffler sense of fractional-order neural networks with piecewise constant arguments. According to the boundedness of activation functions and the model of fractional-order neural networks with piecewise constant arguments, n pairs of bounded functions are constructed. On the basis of the sign of the n pairs of bounded functions, the n-dimensional state space is divided into ∏ i = 1 n ( 2 L i + 1 ) regions. Sufficient conditions are derived to ensure that there exists at leat one equilibrium point in each one of these regions. In addition, ∏ i = 1 n ( L i + 1 ) equilibrium points are locally Mittag-Leffler stable. Two numerical examples are provided to demonstrate the validity of the theoretical results.