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Global asymptotic stability of cellular neural networks with proportional delays

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Abstract

Proportional delay, which is different from distributed delay, is a kind of unbounded delay. The proportional delay system as an important mathematical model often rises in some fields such as physics, biology systems, and control theory. In this paper, the uniqueness and the global asymptotic stability of equilibrium point of cellular neural networks with proportional delays are analyzed. By using matrix theory and constructing suitable Lyapunov functional, delay-dependent and delay-independent sufficient conditions are obtained for the global asymptotic stability of cellular neural networks with proportional delays. These results extend previous works on these issues for the delayed cellular neural networks. Two numerical examples and their simulation are given to illustrate the effectiveness of obtained results.

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Acknowledgments

The project is supported by the National Science Foundation of China (No. 61374009), Tianjin Municipal Education commission (No. 20100813) and Foundation for Doctors of Tianjin Normal University (No. 52LX34).

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  1. School of Mathematics Science, Tianjin Normal University, Tianjin, 300387, China

    Liqun Zhou

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  1. Liqun Zhou
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Correspondence to Liqun Zhou.

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Zhou, L. Global asymptotic stability of cellular neural networks with proportional delays. Nonlinear Dyn 77, 41–47 (2014). https://doi.org/10.1007/s11071-014-1271-y

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  • DOI: https://doi.org/10.1007/s11071-014-1271-y

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