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Lai, Xianghong; Yao, Tianxiang

Exponential stability of impulsive delayed reaction-diffusion cellular neural networks via Poincaré integral inequality. (English) Zbl 1273.35287

Abstr. Appl. Anal. 2013, Article ID 131836, 10 p. (2013).
Summary: This work is devoted to the stability study of impulsive cellular neural networks with time-varying delays and reaction-diffusion terms. By means of new Poincaré integral inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some novel and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The provided stability criteria are applicable to Dirichlet boundary condition and show that not only the reaction-diffusion coefficients but also the regional features including the boundary and dimension of spatial variable can influence the stability. Two examples are finally illustrated to demonstrate the effectiveness of our obtained results.

Cited in 2 Documents

MSC:

35R10 Partial functional-differential equations
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\textit{X. Lai} and \textit{T. Yao}, Abstr. Appl. Anal. 2013, Article ID 131836, 10 p. (2013; Zbl 1273.35287)
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