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Phase and anti-phase synchronizations of fractional order hyperchaotic systems with uncertainties and external disturbances using nonlinear active control method

  • Vijay K. Yadav
  • S. K. Agrawal
  • M. Srivastava
  • S. Das
Article

Abstract

In this paper, the phase and anti-phase synchronizations between fractional order hyperchaotic Lu and 4D integral order systems with parametric uncertainties and disturbances are studied using nonlinear active control method. A new lemma is used to design the controller. Numerical simulations are presented to demonstrate the effectiveness of the method to synchronize and anti-synchronize the fractional order hyperchaotic systems. The striking feature of the article is the comparison of time of synchronization and anti-synchronization with and without the presence of uncertainties and external disturbances through graphical presentations for different particular cases.

Keywords

Fractional derivative Hyperchaotic systems Nonlinear active control method Lyapunov stability Synchronization Phase-synchronization  Antiphase-synchronization 

Notes

Acknowledgments

The authors express their heartfelt thanks to the revered reviewers for their valuable suggestions for the improvement of the article. The first author acknowledges the financial support from the UGC, New Delhi, India under the JRF scheme.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Vijay K. Yadav
    • 1
  • S. K. Agrawal
    • 2
  • M. Srivastava
    • 1
  • S. Das
    • 1
  1. 1.Department of Mathematical SciencesIndian Institute of Technology (BHU)VaranasiIndia
  2. 2.Department of Applied SciencesBharati Vidyapeeth’s College of EngineeringDelhiIndia

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