Finite/fixed-time synchronization for Markovian complex-valued memristive neural networks with reaction-diffusion terms and its application

This paper pays attention to the synchronization issue of complex-valued memristive neural networks (CVMNNs) that contain reaction-diffusion terms and Markovian jump parameters. To better meet the needs of some practical projects, the problem of synchronization investigated in this paper is defined in finite time and fixed time; namely, by designing a suitable controller, the synchronization error system can converge to zero in a finite/fixed time. Additionally, by combining Lyapunov-Krasovskii functional theory and algebraic inequality methods, a novel criterion of finite/fixed-time synchronization for proposed drive and response systems is derived. Note that the finite-time and fixed-time synchronization criteria are integrated into a unified theorem. Finally, two examples are provided, one is a simple numerical example to account for the feasibility of main results, the other realizes the application of this paper in establishing a spatiotemporal chaotic cryptosystem for image encryption, and the proposed cryptosystem has been illustrated that it has obvious advantages of large key space and high security by simulation results. (C) 2020 Published by Elsevier B.V.