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

TL;DR

This paper develops new control strategies using pinning impulse and hybrid controllers to achieve asymptotic and finite-time cluster synchronization in time-varying delayed neural networks, with theoretical criteria and practical examples.

Contribution

It introduces novel sufficient criteria for cluster synchronization using Lyapunov methods and hybrid control, addressing time delays and control cost reduction.

Findings

Established criteria for asymptotic cluster synchronization.

Derived conditions for finite-time cluster synchronization.

Validated results with a practical example.

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.