Abstract
In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.
Highlights
Since Chua proposed the cellular neural networks (CNNs) in the 1980s [1], the neural network models have been widely studied and applied in the fields of signal recognition, image processing, pattern classification, and so on. All these applications rely on the dynamic behaviors of neural networks. e key to using neural networks to solve these problems is that the neural network must be globally dynamic stable; that is to say, each of its loci must converge to a unique balance
E main contributions of this work are as follows: (I) We have formulated a class of new neural network models which assembles nonautonomous neural networks, reaction-diffusion cellular neural networks with time-varying delays, impulses, and the Dirichlet boundary conditions
We establish a series of sufficient conditions to ensure the global exponential stability of systems (1a)–(1d)
Summary
Since Chua proposed the cellular neural networks (CNNs) in the 1980s [1], the neural network models have been widely studied and applied in the fields of signal recognition, image processing, pattern classification, and so on. In [17, 18], the authors considered the exponential stability of reaction-diffusion neural networks with time delays in general spatial regions and obtained some new sufficient conditions for system stability by using Poincare’s inequality technique. Erefore, it is of great significance to study the stability and periodicity of neural network models with dynamic impulses, time delays, and reaction-diffusion terms. We introduce a class of new nonautonomous impulsive neural networks with time-varying delays and reaction-diffusion terms as follows: zzp(t, zt x) m. (I) We have formulated a class of new neural network models which assembles nonautonomous neural networks, reaction-diffusion cellular neural networks with time-varying delays, impulses, and the Dirichlet boundary conditions.
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