Abstract
A class of fuzzy Cohen‐Grossberg neural networks with distributed delay and variable coefficients is discussed. It is neither employing coincidence degree theory nor constructing Lyapunov functionals, instead, by applying matrix theory and inequality analysis, some sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and global exponential stability of the periodic solution for the fuzzy Cohen‐Grossberg neural networks. The method is very concise and practical. Moreover, two examples are posed to illustrate the effectiveness of our results.
Highlights
Cohen-Grossberg neural networks CGNNs and fuzzy cellular neural networks FCNNs with their various models have attracted many scholars’ attention due to their potential applications in classification, associative memory, parallel computation, image processing, and pattern recognition, especially in white blood cell detection and in the solution of some optimization problems, presented by 1–22
It is worth noting that studies have indicated FCNNs’ potential applications in many fields such as image and signal processing, pattern recognition, white blood cell detection, and so on
Some results on stability have been derived from the FCNNs models without or with time delays; see 16–21
Summary
Cohen-Grossberg neural networks CGNNs and fuzzy cellular neural networks FCNNs with their various models have attracted many scholars’ attention due to their potential applications in classification, associative memory, parallel computation, image processing, and pattern recognition, especially in white blood cell detection and in the solution of some optimization problems, presented by 1–22. In 14 , the authors integrated fuzzy logic into the structure of CGNNs, maintained local connectedness among cells which are called fuzzy Cohen-Grossberg neural networks FCGNNs , and studied impulsive effects on stability of FCGNNs with time-varying delays. 1. In 5 , following the idea of vector Lyapunov function, M-matrix theory, and inequality technique, authors studied Cohen-Grossberg neural network model with both time-varying and continuously distributed delays and obtained several sufficient conditions to ensure the existence, uniqueness, and global exponential stability of equilibrium point for this system. Motivated by the above discussions, the objective of this paper is to study the periodic oscillatory solutions of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients and to obtain several novel sufficient conditions to ensure the existence, uniqueness, global attractivity, and global exponential stability of periodic solutions for the model with periodic external inputs.
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