Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality | Zendy

Xianghong Lai | Zendy; Tianxiang Yao | Zendy

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Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality

Author(s) -

Xianghong Lai,

Tianxiang Yao

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/131836

Subject(s) - mathematics , exponential stability , stability (learning theory) , boundary (topology) , reaction–diffusion system , dimension (graph theory) , gronwall's inequality , poincaré inequality , diffusion , exponential function , work (physics) , mathematical analysis , inequality , pure mathematics , computer science , nonlinear system , mechanical engineering , physics , quantum mechanics , machine learning , engineering , thermodynamics

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

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