Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincarè inequality. Issue 7 (May 2017) - Li, Ruoxia; Cao, Jinde; Alsaedi, Ahmed; Ahmad, Bashir
Highlights: We make the first attempt to verify the passivity performance of reaction-diffusion Cohen-Grossberg neutral networks. By employing Hardy-Poincarè inequality, a more accurate estimation of the reaction-diffusion term is presented. The proposed criteria not only depends on the system parameters, reaction-diffusion coefficients but also on the regional feature. Abstract: In this paper, we formulate and investigate the passivity analysis of delayed reaction-diffusion neural networks with Cohen-Grossberg type. The derivative of the Lyapunov-Krasovskii functional was estimated by the new agencies of Hardy-Poincarè inequality and some analysis techniques. Subsequently, some new and concise conditions to check the passivity of the given Cohen-Grossberg neural networks were summarized. The proposed criteria not only depends on the system parameters, reaction-diffusion coefficients but also on the regional feature. Furthermore, as corollaries, some sufficient schemes are provided to achieve passive and exponential passive of delayed Cohen-Grossberg neural networks without reaction-diffusion term. The results obtained in this paper generalize and improve many known results. Finally, two numerical examples and its simulations are proposed to show the effectiveness and merits of the improved theoretical results.