Title: Adaptive control to synchronize and anti-synchronize two identical time delay Bhalekar-Gejji chaotic systems with unknown parameters

Authors: Mohammad Shahzad; Azizan Bin Saaban; Adyda Binti Ibrahim; Israr Ahmad

Addresses: College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman ' School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Malaysia ' School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Malaysia ' College of Applied Sciences Nizwa, Ministry of Higher Education, Sultanate of Oman; School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Malaysia

Abstract: Based on the Lyapunov-Krasovskii functional theory and using the adaptive control, the work of this paper addresses the globally and asymptotically stable synchronisation and anti-synchronisation between two nearly identical time delay Bhalekar-Gejji chaotic systems in the presence of unknown parameters. Using the drive-response system synchronisation and anti-synchronisation schemes and based on the adaptive control, some algebraic sufficient conditions are derived that guarantee the globally and asymptotically stable synchronisation and anti-synchronisation between two identical time-delay Bhalekar-Gejji chaotic systems. Accordingly, appropriate update laws are designed to identify the fully unknown parameters. It has been shown that the proposed approach has an excellent transient performance in comparison with some noting existing results. Numerical simulations are given to verify and test the effectiveness of the current study.

Keywords: synchronisation; anti-synchronisation; Lyapunov-Krasovskii functional theory; adaptive control; time delay; Bhalekar-Gejji chaotic system; chaos; unknown parameters; numerical simulation.

DOI: 10.1504/IJAAC.2015.070957

International Journal of Automation and Control, 2015 Vol.9 No.3, pp.211 - 227

Received: 12 Feb 2015
Accepted: 02 May 2015

Published online: 03 Aug 2015 *

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