Abstract
This work addresses the stability study for stochastic cellular neural networks with time-varying delays. By utilizing the new research technique of the fixed point theory, we find some new and concise sufficient conditions ensuring the existence and uniqueness as well as mean-square global exponential stability of the solution. The presented algebraic stability criteria are easily checked and do not require the differentiability of delays. The paper is finally ended with an example to show the effectiveness of the obtained results.
Highlights
Cellular neural networks (CNNs), firstly proposed by Chua and Yang in 1988 [1, 2], have become a research focus owing to their numerous successful applications in various fields such as optimization, linear and nonlinear programming, associative memory, pattern recognition, and computer vision
Taking into account the finite switching speed of amplifiers in the implementation of neural networks, we see that the time delays are inevitable and a new important model, namely, delayed cellular neural networks (DCNNs), is put forward
In [27–29], Luo used the fixed point theory to study the exponential stability of mild solutions for stochastic partial differential equations with bounded delays and with infinite delays
Summary
Cellular neural networks (CNNs), firstly proposed by Chua and Yang in 1988 [1, 2], have become a research focus owing to their numerous successful applications in various fields such as optimization, linear and nonlinear programming, associative memory, pattern recognition, and computer vision. The fixed point theory is successfully applied by Burton and other authors to investigate the stability of deterministic systems, followed by some valid conclusions presented; for example, see the monograph [13] and the papers [14–25] This new idea is developed to discuss the stability of stochastic (delayed) differential equations, turning out to be effective for the stability analysis of dynamical systems with delays and stochastic effects; see [26– 32]. In [27–29], Luo used the fixed point theory to study the exponential stability of mild solutions for stochastic partial differential equations with bounded delays and with infinite delays. In [30, 31, 33–35], Sakthivel et al used the fixed point theory to investigate the asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with bounded delays and with infinite delays. Some algebraic stability criteria are presented, which are checked and do not require the differentiability of delays, let alone the monotone decreasing behavior of delays
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