Nonlinear Dynamics

, Volume 74, Issue 4, pp 1169–1181 | Cite as

Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography

  • P. Muthukumar
  • P. Balasubramaniam
Original Paper


In this paper, the stability conditions and chaotic behaviors of new different fractional orders of reverse butterfly-shaped dynamical system are analytically and numerically investigated. Designing an appropriate feedback controller, the fractional order chaotic system is synchronized. Applying the synchronized fractional order systems in digital cryptography, a well secured key system is obtained. The numerical simulations are given to validate the correctness of the proposed synchronized fractional order chaotic systems and proposed key system.


Synchronization Fractional order system Fibonacci numbers Cryptography 



This work is supported by the University Grants Commission-Basic Science Research, Government of India, New Delhi. The authors are very thankful to the editors and anonymous reviewers for their careful reading, constructive comments, and fruitful suggestions to improve this manuscript.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Gandhigram Rural InstituteDeemed University GandhigramDindigulIndia

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