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October  2013, 18(8): 2019-2028. doi: 10.3934/dcdsb.2013.18.2019

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

Guoliang Cai 1, , Lan Yao 1, , Pei Hu 1, and  Xiulei Fang 1,

1. 

Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China, China, China, China

Received  December 2012 Revised  June 2013 Published  July 2013

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.
Keywords: Full state hybrid function projective synchronization (FSHFPS), Lyapunov stability theory, financial hyperchaotic system..
Mathematics Subject Classification: Primary: 34D20, 37N40, 93C1.
Citation: Guoliang Cai, Lan Yao, Pei Hu, Xiulei Fang. Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2019-2028. doi: 10.3934/dcdsb.2013.18.2019
References:
[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), 11-20 doi: 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), 1457-1464 doi: 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), 213-218 doi: 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), 231-237 doi: 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), 209-216 doi: 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), 2171-2182 doi: 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

show all references

References:
[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), 11-20 doi: 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), 1457-1464 doi: 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), 213-218 doi: 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), 231-237 doi: 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), 209-216 doi: 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), 2171-2182 doi: 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

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