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Hyperchaos control and adaptive synchronization with uncertain parameter for fractional-order Mathieu–van der Pol systems

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Abstract

In this paper, we have discussed the local stability of the Mathieu–van der Pol hyperchaotic system with the fractional-order derivative. The fractional Routh–Hurwitz stability conditions were provided and were used to discuss the stability. Feedback control method was used to control chaos in the Mathieu–van der Pol system with fractional-order derivative and after controlling the chaotic behaviour of the system the synchronization between the fractional-order hyperchaotic Mathieu–van der Pol system and controlled system was introduced. In this study, modified adaptive control methods with uncertain parameters at various equilibrium points were used. Also the analysis of control time with respect to different fractional-order derivatives is the key feature of this paper. Numerical simulation results achieved using Adams–Boshforth–Moulton method show that the method is effective and reliable.

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Acknowledgement

The authors of this article express their heartfelt thanks to the reviewers for their valuable suggestions for the improvement of the article.

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Authors and Affiliations

  1. Department of Mathematics and Basic Science, NIIT University, Neemrana, 301 705, India

    KUMAR VISHAL

  2. Department of Applied Sciences, Bharati Vidyapeeth’s College of Engineering, New Delhi, 110 063, India

    SAURABH K AGRAWAL

  3. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221 005, India

    SUBIR DAS

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  1. KUMAR VISHAL
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  2. SAURABH K AGRAWAL
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  3. SUBIR DAS
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Correspondence to KUMAR VISHAL.

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VISHAL, K., AGRAWAL, S.K. & DAS, S. Hyperchaos control and adaptive synchronization with uncertain parameter for fractional-order Mathieu–van der Pol systems. Pramana - J Phys 86, 59–75 (2016). https://doi.org/10.1007/s12043-015-0989-5

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  • DOI: https://doi.org/10.1007/s12043-015-0989-5

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