Title: Adaptive combination synchronisation of unknown chaotic Lorenz, Lü, Rössler and Chen systems

Authors: M. Mossa Al-sawalha; Y. Jawarneh; Israr Ahmad; Mohd Taib Shatnawi

Addresses: Department of Mathematics, University of Ha'il, 2440, Saudi Arabia ' Department of Mathematics, University of Ha'il, 2440, Saudi Arabia ' Department of General Requirements, College of Applied Sciences Nizwa, 611, Oman ' Department of Basic Science, Al-Huson University College, Al-Balqa Applied University, Irbid, 21510, Jordan

Abstract: This paper studies the adaptive combined synchronisation (ACS) of different unknown chaotic systems. In the proposed scheme, the state vectors of a response system synchronise with the corresponding state vectors of the combined dual drive systems. The Lyapunov stability theory proves the asymptotic stability of the closed loop system at the origin. This work provides parameter update laws that estimate the actual values of unknown parameters. Important numerical simulation is included to show the effectiveness of the propose synchronisation scheme.

Keywords: combined synchronisation; Lyapunov stability theory; adaptive control technique; unknown parameters; Lorenz system; Lü system; Rössler system; Chen system.

DOI: 10.1504/IJMIC.2020.115391

International Journal of Modelling, Identification and Control, 2020 Vol.36 No.1, pp.34 - 41

Received: 05 Mar 2020
Accepted: 20 Jul 2020

Published online: 01 Jun 2021 *

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