Abstract
This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.
Highlights
Cohen-Grossberg neural networks (CGNNs) were introduced by Cohen and Grossberg in 1983 [1] and have been a hot topic due to their important applications in various fields such as parallel computation, associative memory, image processing, and optimization problems.By reason that time delays are unavoidably encountered for the finite switching speed of neurons and amplifiers in the implementation of neural networks, a more powerful model of delayed Cohen-Grossberg neural networks (DCGNNs) is afterwards proposed
At t = tk (k = 0, 1, 2, . . .), we find by the use of (24)
Theorems 5–11 can be regarded as the special cases of Theorem 12
Summary
Cohen-Grossberg neural networks (CGNNs) were introduced by Cohen and Grossberg in 1983 [1] and have been a hot topic due to their important applications in various fields such as parallel computation, associative memory, image processing, and optimization problems. Besides impulsive effects, we have to recognize that diffusion effects are nonignorable in reality as diffusion is unavoidable when electrons are moving in asymmetric electromagnetic fields On this account, the model of neural networks with both impulses and diffusion should be more effective for describing the evolutionary process of practical systems. The model of neural networks with both impulses and diffusion should be more effective for describing the evolutionary process of practical systems Based on this consideration, we wonder what the influence of diffusion on the stability of CGNNs and DCGNNs is.
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