Global Mittag Leffler stability and synchronization of discrete time fractional order complex valued neural networks with time delay
Without decomposing complex valued systems into real valued systems, this paper investigates existence, uniqueness, global Mittag Leffler stability and global Mittag Leffler synchronization of discrete time fractional order complex valued neural networks (FCVNNs) with time delay. Inspired by Lyapunov's direct method on continuous time systems, a class of discrete time FCVNNs is further discussed by employing the fractional order extension of Lyapunov's direct method. Firstly, by means of contraction mapping theory and Cauchy's inequality, a sufficient condition is presented to ascertain the existence and uniqueness of the equilibrium point for discrete time FCVNNs. Then, based on the theory of discrete fractional calculus, discrete Laplace transform, the theory of complex functions and discrete Mittag Leffler functions, a sufficient condition is established for global Mittag Leffler stability of the proposed networks. Additionally, by applying the Lyapunov's direct method and designing a effective control scheme, the sufficient criterion is derived to ensure the global Mittag Leffler synchronization of discrete time FCVNNs. Finally, two numerical examples are also presented to manifest the feasibility and validity of the obtained results.
Neural Networks