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Delay-Dependent exponential stability for nonlinear reaction-diffusion uncertain Cohen-Grossberg neural networks with partially known transition rates via Hardy-Poincaré inequality

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Abstract

In this paper, stochastic global exponential stability criteria for delayed impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks (CGNNs for short) are obtained by using a novel Lyapunov-Krasovskii functional approach, linear matrix inequalities (LMIs for short) technique, Itô formula, Poincaré inequality and Hardy-Poincaré inequality, where the CGNNs involve uncertain parameters, partially unknown Markovian transition rates, and even nonlinear p-Laplace diffusion (p > 1). It is worth mentioning that ellipsoid domains in ℝm (m ≥ 3) can be considered in numerical simulations for the first time owing to the synthetic applications of Poincaré inequality and Hardy-Poincaré inequality. Moreover, the simulation numerical results show that even the corollaries of the obtained results are more feasible and effective than the main results of some recent related literatures in view of significant improvement in the allowable upper bounds of delays.

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, Yibin, 644007, Sichuan, China

    Ruofeng Rao

  2. Institution of Mathematics, Yibin University, Yibin, 644007, China

    Ruofeng Rao

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  1. Ruofeng Rao
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Correspondence to Ruofeng Rao.

Additional information

This work was supported by the National Basic Research Program of China (No. 2010CB732501), the Scientific Research Fund of Science Technology Department of Sichuan Province (Nos. 2010JY0057, 2012JYZ010), the Sichuan Educational Committee Science Foundation (Nos. 08ZB002, 12ZB349) and the Scientific Research Fund of Sichuan Provincial Education Department (Nos. 14ZA0274, 08ZB002, 12ZB349).

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Rao, R. Delay-Dependent exponential stability for nonlinear reaction-diffusion uncertain Cohen-Grossberg neural networks with partially known transition rates via Hardy-Poincaré inequality. Chin. Ann. Math. Ser. B 35, 575–598 (2014). https://doi.org/10.1007/s11401-014-0839-7

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  • DOI: https://doi.org/10.1007/s11401-014-0839-7

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