Abstract
In the article, the dynamical behaviours of the full-range cellular neural networks (FRCNNs) with variable coefficients and time-varying delays are considered. Firstly, the improved model of the FRCNNs is proposed, and the existence and uniqueness of the solution are studied by means of differential inclusions and set-valued analysis. Secondly, by using the Hardy inequality, the matrix analysis, and the Lyapunov functional method, we get some criteria for achieving the globally exponential stability (GES). Finally, some examples are provided to verify the correctness of the theoretical results.
Highlights
The research of the cellular neural networks (CNNs) [6, 7] is a hot topic because of powerful parallel and nonlinear processing capabilities and its widespread applications, such as edge detection, image processing, optimization problems, and so on
Many studies have been done to understand the dynamical behaviors of CNNs
The local Hopf bifurcations of tri-neuron neural networks were studied, and the stability of Hopf bifurcations was determined by the Nyquist criterion and the graphical Hopf bifurcation theorem in [36, 37]
Summary
The research of the cellular neural networks (CNNs) [6, 7] is a hot topic because of powerful parallel and nonlinear processing capabilities and its widespread applications, such as edge detection, image processing, optimization problems, and so on These applications depend largely on the stability of CNNs. But not all CNNs are globally stable, some of them exhibit complex dynamic behaviors.
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