Mittag-Leffler stability analysis of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument

Liguang Wan,Ailong Wu

doi:10.1186/s13662-017-1368-y

Abstract

This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. Applying the Lyapunov method, the generalized Gronwall-Bellman inequality, and the theory of fractional-order differential equations, sufficient conditions are presented to guarantee the existence and uniqueness of solution. Besides, the global Mittag-Leffler stability is investigated. The obtained criteria are useful in the analysis and design of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. A numerical example is given to substantiate the validity of the theoretical results.

Highlights

Neural networks have attracted much attention due to their great potential prospectives in various areas, such as signal processing, associative memory, pattern recognition, and so on [ – ]
In [ ], the robust stability about the integer-order Cohen-Grossberg neural networks is explored based on the comparison principle
The dynamic properties of Cohen-Grossberg neural networks can describe the evolution of the competition between species in living nature, where the equilibrium points stand for the survival or extinction of the species

Summary

Introduction

Neural networks have attracted much attention due to their great potential prospectives in various areas, such as signal processing, associative memory, pattern recognition, and so on [ – ]. Inspired by the above discussions, this paper formulates the global Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. The existence and uniqueness of solution for fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument are addressed. Sufficient conditions are derived to guarantee the global Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. The existing approaches for the stability of neural networks cannot be applied straightforwardly to fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. In accordance with the theory of differential equations with deviating argument and in conjunction with the properties of fractional-order calculus, the global Mittag-Leffler stability of such type of neural networks is explored in detail. We consider a general class of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument described by the following fractional-order differential equations:.

Proof Define a Lyapunov function by n

It can be seen that ω