A NOVEL FRACTIONAL-ORDER HYPERCHAOTIC SYSTEM AND ITS SYNCHRONIZATION

Ping Zhou (P. R. China) and Wei Zhu (P. R. China)

Received December 28, 2008

References:

[1] T. L. Carroll and L. M. Pecora, Synchronizing chaotic circuits, IEEE Trans. Circuits Syst. 38(4) (1991), 453-456. [2] K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Electron. Trans. Numer. Anal. 5 (1997), 1-6. [3] K. Diethelm, N. J. Ford and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynam. 29(1-4) (2002), 3-22. [4] K. Diethelm, N. J. Ford and A. D. Freed, Detailed error analysis for a fractional Adams method, Numer. Algorithms 36(1) (2004), 31-52. [5] Z.-M. Ge and C.-Y. Ou, Chaos in a fractional order modified Duffing system, Chaos Solitons Fractals 34(2) (2007), 262-291. [6] I. Grigorenko and E. Grigorenko, Chaotic dynamics of the fractional Lorenz system, Phys. Rev. Lett. 91 (2003), 034101. [7] C. G. Li and G. R Chen, Chaos in the fractional order Chen system and its control, Chaos Solitons Fractals 22(3) (2004), 549-554. [8] C. G. Li and G. R. Chen, Chaos and hyperchaos in the fractional-order Rössler equations, Phys. A 341 (2004), 55-61. [9] C. P. Li, W. H. Deng and D. Xu, Chaos synchronization of the Chua system with a fractional order, Phys. A 360(2) (2006), 171-185. [10] C. G. Li, X. Liao and J. B. Yu, Synchronization of fractional order chaotic systems, Phys. Rev. E 68 (2003), 067203. [11] C. P. Li and G. J. Peng, Chaos in Chen’s system with a fractional order, Chaos Solitons Fractals 22(2) (2004), 443-450. [12] C. P. Li and J. P. Yan, The synchronization of three fractional differential systems, Chaos Solitons Fractals 32(2) (2007), 751-757. [13] L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64(8) (1990), 821-824. [14] M. S. Tavazoei and M. Haeri, A necessary condition for double scroll attractor existence in fractional-order systems, Phys. Lett. A 367(1-2) (2007), 102-113. [15] J. W. Wang, X. H. Xiong and Y. Zhang, Extending synchronization scheme to chaotic fractional-order Chen systems, Phys. A 370(2) (2006), 279-285. [16] J. P. Yan and C. P. Li, On chaos synchronization of fractional differential equations, Chaos Solitons Fractals 32(2) (2007), 725-735. [17] Y. G. Yu and H.-X. Li, The synchronization of fractional-order Rössler hyperchaotic systems, Phys. A 387(5-6) (2008), 1393-1403. [18] T. S. Zhou and C. P. Li, Synchronization in fractional-order differential systems, Phys. D 212(1-2) (2005), 111-125.

Keywords and phrases: hyperchaotic systems, synchronization, fractional-order.