Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms

Abstract In this paper, the multi-weighted coupled neural networks (MWCNN) models with and without reaction-diffusion terms are studied, respectively. Firstly, we analyze the anti-synchronization of MWCNN with and without coupling delays by means of Lyapunov functional approach and some inequality techniques, and put forward some anti-synchronization conditions for the considered networks. Additionally, it is well known that pinning control is a very efficient tool to achieve the anti-synchronization of networks by adopting appropriate pinning controllers to a small fraction of nodes in networks. Therefore, we further investigate the pinning anti-synchronization of the considered networks, and derive some sufficient conditions which ensure that these networks are pinning anti-synchronized. Similarly, anti-synchronization analysis and pinning control for multi-weighted coupled reaction-diffusion neural networks (MWCRDNN) with and without coupling delays are considered, and several anti-synchronization and pinning anti-synchronization criteria for MWCRDNN are established. Lastly, four examples are used to confirm the effectiveness of the derived results.

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