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Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB)

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Abstract

In this paper, a fractional order dynamical system is constructed that exhibits chaotic and reverse chaotic attractors by changing the sign of the one parameter which involves in the existence of the phase reversal function. A new method of fast projective synchronization of fractional order dynamical systems is introduced. An affine cipher is proposed for secure communication based on the solutions of the synchronized fractional order chaotic systems with the support of the sender’s and receiver’s date of birth. The efficiency and security of an affine cipher are analyzed. Numerical simulations are demonstrated to show the feasibility of the presented theory.

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Acknowledgments

This work is supported by the University Grants Commission-Basic Science Research (UGC-BSR), Grant No: F.7-73/2007 (BSR), Government of India, New Delhi. It is also supported by the Project No: UM.C/625/1/HIR/MOHE/13, University of Malaya, Malaysia. The authors are very much thankful to the editors and anonymous reviewers for their careful reading, constructive comments and fruitful suggestions to improve this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Dindigul, Tamil Nadu, India

    P. Muthukumar & P. Balasubramaniam

  2. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 , Kuala Lumpur, Malaysia

    K. Ratnavelu

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  1. P. Muthukumar
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  2. P. Balasubramaniam
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  3. K. Ratnavelu
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Correspondence to P. Balasubramaniam.

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Muthukumar, P., Balasubramaniam, P. & Ratnavelu, K. Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB). Nonlinear Dyn 80, 1883–1897 (2015). https://doi.org/10.1007/s11071-014-1583-y

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  • DOI: https://doi.org/10.1007/s11071-014-1583-y

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