Exponential stability and synchronisation of fuzzy Mittag–Leffler discrete-time Cohen–Grossberg neural networks with time delays

Abstract

Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. Therefore, exponential Euler differences for fractional-order differential models are novel and significant. In allusion to fuzzy Cohen–Grossberg neural networks of fractional order, this paper establishes a Mittag–Leffler Euler difference model on the basis of the constant variation formula in fractional calculus. In the second place, the existence of a unique global bounded solution and equilibrium point is studied by using the contractive mapping principle. Thirdly, global exponential stability and synchronisation of the derived difference models are investigated by employing some inequality techniques and reductio. At last, some illustrative examples and numerical simulations are employed to demonstrate the main results of this paper.