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Designing synchronization schemes for chaotic fractional-order unified systems. (English) Zbl 1142.37332
Summary: Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration.

37D45Strange attractors, chaotic dynamics
34D20Stability of ODE
93D15Stabilization of systems by feedback
Full Text: DOI
[1] Ross, B.: Fractional calculus and its applications. Lecture notes in mathematics (June 1974)
[2] Hilfer, B.: Applications of fractional calculus in physics. (2001) · Zbl 0998.26002
[3] Butzer, P-L.; Westphal, U.: An introduction to fractional calculus. (2000) · Zbl 0987.26005
[4] Kenneth, S. M.; Bertram, R.: An introduction to the fractional calculus and fractional differential equations. (1993) · Zbl 0789.26002
[5] Arena P, Caponetto R, Fortuna L, Porto D. In: Proc of ECCTD, Technical University of Budapest, Budapest, September 1997. p. 1259.
[6] Hartley, T. T.; Lorenzo, C. F.; Qammer, H. K.: IEEE trans circ syst I. 42, 485 (1995)
[7] Li, C. P.; Peng, G. J.: Chaos, solitons & fractals. 22, 443 (2004)
[8] Deng, W. H.; Li, C. P.: Physica A. 353, 61 (2005)
[9] Caputo, M.: Geophys J R astron soc. 13, 529 (1967)
[10] Lü, J.; Chen, G.; Cheng, D.; Čelikovský, S.: Int J bifurcat chaos. 12, 2917 (2002)
[11] Pecora, L. M.; Carroll, T. L.: Phys rev lett. 64, 821 (1990)
[12] Van, J. P.; Li, C. P.: Chaos, solitons & fractals. 23, 1683 (2005)