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arXiv · 2103.09625

Asymptotic and Finite-time Cluster Synchronization of Neural Networks via Two Different Controllers

Juan Cao·Fengli Ren·Dacheng Zhou
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Abstract

In this paper, by using pinning impulse controller and hybrid controller respectively, the research difficulties of asymptotic synchronization and finite time cluster synchronization of time-varying delayed neural networks are studied. On the ground of Lyapunov stability theorem and Lyapunov-Razumikhin method, a novel sufficient criterion on asymptotic cluster synchronization of time-varying delayed neural networks is obtained. Utilizing Finite time stability theorem and hybrid control technology, a sufficient criterion on finite-time cluster synchronization is also obtained. In order to deal with time-varying delay and save control cost, pinning pulse control is introduced to promote the realization of asymptotic cluster synchronization. Following the idea of pinning control scheme, we design a progressive hybrid control to promote the realization of finite time cluster synchronization. Finally, an example is given to illustrate the theoretical results.

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Juan Cao, Fengli Ren, Dacheng Zhou. 2021-03-17. Asymptotic and Finite-time Cluster Synchronization of Neural Networks via Two Different Controllers. https://arxiv.org/abs/2103.09625

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