Adaptive add order synchronization and anti-synchronization of fractional order chaotic systems with fully unknown parameters

Volume 10, Issue 5, pp 2592--2606 http://dx.doi.org/10.22436/jnsa.010.05.26

Publication Date: May 25, 2017 Submission Date: March 26, 2017

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Authors

M. M. Al-sawalha - Mathematics Department, Faculty of Science, University of Hail, Kingdom of Saudi Arabia. M. Ghazel - Mathematics Department, Faculty of Science, University of Hail, Kingdom of Saudi Arabia. O. Y. Ababneh - School of Mathematics, Zarqa University, Zarqa, Jordan. M. Shoaib - Abu Dhabi Men’s College, Higher Colleges of Technology, P. O. Box 25035, Abu Dhabi, United Arab Emirates.

Abstract

In this paper, an adaptive control scheme is developed to study the add order synchronization and the add order antisynchronization behavior between two different dimensional fractional order chaotic systems with fully uncertain parameters. This design of adaptive controller is based on the Lyapunov stability theory. Analytic expression for the controller with its adaptive laws of parameters is shown. The adaptive add order synchronization and add order anti-synchronization between two fractional order chaotic systems are used to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are used to verify the results.

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Keywords

• Add order
• synchronization
• anti-synchronization
• adaptive control
• unknown parameters
• Lyapunov stability theory.

MSC

•  93C10
•  93C95

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