Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 13, Issue 3, Pages 1441-1450Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2011.11.008
Keywords
Fractional order; Hyperchaotic system; Projective synchronization (PS); Modified generalized projective synchronization (MGPS); Secure communication
Categories
Funding
- National Natural Science Foundation of China [61004006, 60873133]
- Natural Science Foundation of Henan Province, China [112300410009]
- Foundation for University Young Key Teacher Program of Henan Province, China [2011GGJS-025]
- Natural Science Foundation of Educational Committee of Henan Province, China [2011A520004]
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This paper presents a new fractional-order hyperchaotic system. The chaotic behaviors of this system in phase portraits are analyzed by the fractional calculus theory and computer simulations. Numerical results have revealed that hyperchaos does exist in the new fractional-order four-dimensional system with order less than 4 and the lowest order to have hyperchaos in this system is 3.664. The existence of two positive Lyapunov exponents further verifies our results. Furthermore, a novel modified generalized projective synchronization (MGPS) for the fractional-order chaotic systems is proposed based on the stability theory of the fractional-order system, where the states of the drive and response systems are asymptotically synchronized up to a desired scaling matrix. The unpredictability of the scaling factors in projective synchronization can additionally enhance the security of communication. Thus MGPS of the new fractional-order hyperchaotic system is applied to secure communication. Computer simulations are done to verify the proposed methods and the numerical results show that the obtained theoretic results are feasible and efficient. (C) 2011 Elsevier Ltd. All rights reserved.
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