Mittag-Leffler stability and synchronization of discrete-time quaternion valued delayed neural networks with fractional order and its application

This paper discusses the problem of Mittag-Leffler stability and synchronization for discrete-time fractional-order delayed quaternion valued neural networks (DTFODQVNN). Firstly, a criterion is achieved to ensure the existence and uniqueness of the equilibrium point (EP) of DTFODQVNN through applying Brouwer's fixed-point theory. Secondly, based on a Lyapunov function and a new discrete fractional inequality, the stability condition is established by employing a linear matrix inequality approach. In addition, by constructing a proper controller, drive-response synchronization is investigated by means of deploying Lyapunov direct method (LDM). Finally, two examples with simulations test the correctness of the acquired results. Moreover, image encryption is considered as an application based on the chaotic DTFODQVNN.