Article Contents
Article Contents

Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters

• This paper further investigates a new type synchronization called full state hybrid function projective synchronization (FSHFPS). Based on the Lyapunov stability theory, the adaptive control law and the parameter update laws are derived to make FSHFPS between two financial hyperchaotic systems. And FSHFPS of financial hyperchaotic systems is first studied in this paper. The method is successfully applied to the synchronization between two identical financial hyperchaotic systems and two different financial hyperchaotic systems when the parameters unknown. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.
Mathematics Subject Classification: Primary: 34D20, 37N40, 93C10.

 Citation:

•  [1] L. M.Park and T. L.Carroll, Synchronization in chaotic systems Phys. Rev. Lett. 64 (1990), 821-823.doi: 10.1103/PhysRevLett.64.821. [2] E. H. Park, M. A. Zaks and J. Kurths, Phase synchronization in the forced Lorenz system Phys. Rev. E. 60 (1990), 6627-2238.doi: 10.1103/PhysRevE.60.6627. [3] Z. B. Li and X. S. Zhao, Generalized function projective synchronization of two different hyperchaotic systems with unknown parameters Nonlinear Anal. Real World Appl. 12 (2011), 2607-2615.doi: 10.1016/j.nonrwa.2011.03.009. [4] H. N. Agiza, Choas synchronization of Lüdynamical system Nonlinear Anal. 58 (2004), 11-20doi: 10.1016/j.na.2004.04.002. [5] G. L. Cai, P. Hu and Y. X. Li, Modified function lag projective synchronization of a financial hyperchaotic system Nonlinear Dyn. 69 (2012), 1457-1464doi: 10.1007/s11071-012-0361-y. [6] G. L. Cai, H. X. Wang and S. Zheng, Adaptive function projective synchronization of two different hyperchaotic systems with unknown parameters Chin. J. Phys. 47 (2009), 662-669 [7] D. L. Chen, J. T. Sun and C. S. Huang, Impulsive control and synchronization of general chaotic system Chaos Solitons Fractals 38 (2006), 213-218doi: 10.1016/j.chaos.2005.05.057. [8] M. F. Hu, Z. F. Xu, R. Zhang and A. H. Hu, Parameters identification and adaptive full state hypbrid projective synchronization of chaotic systems Physica A. 361 (2007), 231-237doi: 10.1016/j.physleta.2006.08.092. [9] D. Guégan, Chaos in economics and finance Annu Rev Control 33 (2009), 89-93 [10] Q. Gao and J. H. Ma, Chaos and Hopf bifurcation of a finance system Nonlinear Dyn. 58 (2009), 209-216doi: 10.1007/s11071-009-9472-5. [11] H. J. Yu, G. L. Cai and Y. X. Li, Dynamic analysis and control of a new hyperchaotic finance system Nonlinear Dyn. 67 (2012), 2171-2182doi: 10.1007/s11071-011-0137-9. [12] J. Ding, W. G. Yang and H. X. Yao, A new Modified Hyperchaotic Finance System and its Control, International Journal of Nonlinear Science Nonlinear Dyn. 8 (2009), 59-66