Existence and global exponential stability of anti-periodic solutions for competitive neural networks with delays in the leakage terms on time scales

Anti-periodic motion and mean-square exponential convergence of nonlocal discrete-time stochastic competitive lattice neural networks with fuzzy logic

This paper firstly establishes the discrete-time lattice networks for nonlocal stochastic competitive neural networks with reaction diffusions and fuzzy logic by employing a mix techniques of finite difference to space variables and Mittag-Leffler time Euler difference to time variable. The proposed networks consider both the effects of spatial diffusion and fuzzy logic, whereas most of the existing literatures focus only on discrete-time networks without spatial diffusion. Firstly, the existence of a unique ω-anti-periodic in distribution to the networks is addressed by employing Banach contractive mapping principle and the theory of stochastic calculus. Secondly, global exponential convergence in mean-square sense to the networks is discussed on the basis of constant variation formulas for sequences. Finally, an illustrative example is used to show the feasible of the works in the current paper with the help of MATLAB Toolbox. The work in this paper is pioneering in this regard and it has created a certain research foundations for future studies in this area.