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Complex modified projective synchronization of two chaotic complex nonlinear systems

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Abstract

In this paper, we present a novel type of synchronization called complex modified projective synchronization (CMPS) and study it to a system of two chaotic complex nonlinear 3-dimensional flows, possessing chaotic attractors. Based on the Lyapunov function approach, a scheme is designed to achieve CMPS for such pairs of (either identical or different) complex systems. Analytical expressions for the complex control functions are derived using this scheme to achieve CMPS. This type of complex synchronization is considered as a generalization of several kinds of synchronization that have appeared in the recent literature. The master and slave chaotic complex systems achieved CMPS can be synchronized through the use of a complex scale matrix. The effectiveness of the obtained results is illustrated by a studying two examples of such coupled chaotic attractors in the complex domain. Numerical results are plotted to show the rapid convergence of modulus errors to zero, thus demonstrating that CMPS is efficiently achieved.

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Acknowledgements

The authors would like to express their sincere appreciation to the reviewers for their helpful comments, which helped us improve the presentation of the paper.

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  1. Gamal M. Mahmoud

    Present address: Department of Mathematics, Faculty of Science, Assiut University, Assiut, 71516, Egypt

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Taibah University, P.O. Box 344, Al-Madeenah Al-Munawwarah, Kingdom of Saudi Arabia

    Gamal M. Mahmoud

  2. Department of Mathematics, Faculty of Science, Sohag University, Sohag, 82524, Egypt

    Emad E. Mahmoud

  3. College of Applied Medical Sciences, Taif University, Turabah, Kingdom of Saudi Arabia

    Emad E. Mahmoud

Authors
  1. Gamal M. Mahmoud
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  2. Emad E. Mahmoud
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Correspondence to Emad E. Mahmoud.

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Mahmoud, G.M., Mahmoud, E.E. Complex modified projective synchronization of two chaotic complex nonlinear systems. Nonlinear Dyn 73, 2231–2240 (2013). https://doi.org/10.1007/s11071-013-0937-1

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  • DOI: https://doi.org/10.1007/s11071-013-0937-1

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