Stability Analysis of Fractional Order Complex-Valued Memristive Neural Networks with Time Delays

This paper presents a theoretical results on the existence, uniqueness of equilibrium point for a class of fractional order complex-valued delayed memristive neural networks, subsequently, its stability analysis are also considered. In a complex-valued recurrent neural networks, the states, connection weights, as well as activation functions are all defined in complex domain, thus, it is an extension of real-valued system. In this paper, by means of an appropriate Lyapunov functional, contraction mapping theory and nonlinear measure method, some sufficient conditions are presented to ascertain the existence, uniqueness and stability of the equilibrium point for the given fractional order complex-valued systems. The obtained results can be easily applied to the complex-valued neural networks whether their activation functions are expressed by separating their real and imaginary parts or not. Finally, simulation examples are presented to show the usefulness of our theoretical results.