Asymptotic and finite-time cluster synchronization of neural networks via two different controllers

Juan Cao; Fengli Ren; Dacheng Zhou

doi:10.3934/dcdsb.2022005

Article Contents

2022, Volume 27, Issue 11: 6465-6480. Doi: 10.3934/dcdsb.2022005

This issue Previous Article On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations Next Article Attractors of the Klein-Gordon-Schrödinger lattice systems with almost periodic nonlinear part

Asymptotic and finite-time cluster synchronization of neural networks via two different controllers

1.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, MO 210016, China
2.
School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, MO 200444, China

^* Corresponding author: Fengli Ren
^* Corresponding author: Fengli Ren

Received: May 31, 2021

Revised: August 31, 2021

Early access: January 2022

Published: October 2022

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Abstract

In this paper, by using a pinning impulse controller and a 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.

Keywords:

Mathematics Subject Classification: Primary: 93C10, 93C27; Secondary: 05C82.

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Figure 1. The error dynamic trajectory when $ i = 1, 2 $ without controller

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Figure 2. The error dynamic trajectory when $ i = 3, 4, 5 $ without controller

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Figure 3. The error dynamic trajectory when $ i = 1, 2 $ with the pinning impulsive controllers (6)

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Figure 4. The error dynamic trajectory when $ i = 3, 4, 5 $ with the pinning impulsive controllers (6)

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Figure 5. The error dynamic trajectory $ i = 1, 2 $ with the hybrid controllers (23)

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Figure 6. The error dynamic trajectory when $ i = 3, 4, 5 $ with the hybrid controllers (23)

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