Stability in cellular neural networks with a piecewise constant argument

Date

2010-03-01

Author

Akhmet, Marat
Yılmaz, Elanur

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In this paper, by using the concept of differential equations with piecewise constant arguments of generalized type [1-4], a model of cellular neural networks (CNNs) [5,6] is developed. The Lyapunov-Razumikhin technique is applied to find sufficient conditions for the uniform asymptotic stability of equilibria. Global exponential stability is investigated by means of Lyapunov functions. An example with numerical simulations is worked out to illustrate the results.

Subject Keywords

Cellular neural networks, Differential equations with a piecewise constant argument of generalized type, Lyapunov-Razumikhin technique, Method of Lyapunov functions, Linear matrix inequality

URI

https://hdl.handle.net/11511/31915

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2009.10.021

Collections

Graduate School of Social Sciences, Article

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LYAPUNOV-RAZUMIKHIN METHOD FOR DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT Akhmet, Marat (2009-10-01) At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.
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Citation Formats

M. Akhmet and E. Yılmaz, “Stability in cellular neural networks with a piecewise constant argument,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 2365–2373, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31915.