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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 & 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), 64 (1990), 821.  doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[2]

E. H. Park, M. A. Zaks and J. Kurths, Phase synchronization in the forced Lorenz system, Phys. Rev. E. 60 (1990), 60 (1990), 6627.  doi: 10.1103/PhysRevE.60.6627.  Google Scholar

[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), 12 (2011), 2607.  doi: 10.1016/j.nonrwa.2011.03.009.  Google Scholar

[4]

H. N. Agiza, Choas synchronization of Lüdynamical system, Nonlinear Anal. 58 (2004), 58 (2004), 11.  doi: 10.1016/j.na.2004.04.002.  Google Scholar

[5]

G. L. Cai, P. Hu and Y. X. Li, Modified function lag projective synchronization of a financial hyperchaotic system, Nonlinear Dyn. 69 (2012), 69 (2012), 1457.  doi: 10.1007/s11071-012-0361-y.  Google Scholar

[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), 47 (2009), 662.   Google Scholar

[7]

D. L. Chen, J. T. Sun and C. S. Huang, Impulsive control and synchronization of general chaotic system, Chaos Solitons Fractals 38 (2006), 38 (2006), 213.  doi: 10.1016/j.chaos.2005.05.057.  Google Scholar

[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), 361 (2007), 231.  doi: 10.1016/j.physleta.2006.08.092.  Google Scholar

[9]

D. Guégan, Chaos in economics and finance, Annu Rev Control 33 (2009), 33 (2009), 89.   Google Scholar

[10]

Q. Gao and J. H. Ma, Chaos and Hopf bifurcation of a finance system, Nonlinear Dyn. 58 (2009), 58 (2009), 209.  doi: 10.1007/s11071-009-9472-5.  Google Scholar

[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), 67 (2012), 2171.  doi: 10.1007/s11071-011-0137-9.  Google Scholar

[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), 8 (2009), 59.   Google Scholar

show all references

References:
[1]

L. M.Park and T. L.Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990), 64 (1990), 821.  doi: 10.1103/PhysRevLett.64.821.  Google Scholar

[2]

E. H. Park, M. A. Zaks and J. Kurths, Phase synchronization in the forced Lorenz system, Phys. Rev. E. 60 (1990), 60 (1990), 6627.  doi: 10.1103/PhysRevE.60.6627.  Google Scholar

[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), 12 (2011), 2607.  doi: 10.1016/j.nonrwa.2011.03.009.  Google Scholar

[4]

H. N. Agiza, Choas synchronization of Lüdynamical system, Nonlinear Anal. 58 (2004), 58 (2004), 11.  doi: 10.1016/j.na.2004.04.002.  Google Scholar

[5]

G. L. Cai, P. Hu and Y. X. Li, Modified function lag projective synchronization of a financial hyperchaotic system, Nonlinear Dyn. 69 (2012), 69 (2012), 1457.  doi: 10.1007/s11071-012-0361-y.  Google Scholar

[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), 47 (2009), 662.   Google Scholar

[7]

D. L. Chen, J. T. Sun and C. S. Huang, Impulsive control and synchronization of general chaotic system, Chaos Solitons Fractals 38 (2006), 38 (2006), 213.  doi: 10.1016/j.chaos.2005.05.057.  Google Scholar

[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), 361 (2007), 231.  doi: 10.1016/j.physleta.2006.08.092.  Google Scholar

[9]

D. Guégan, Chaos in economics and finance, Annu Rev Control 33 (2009), 33 (2009), 89.   Google Scholar

[10]

Q. Gao and J. H. Ma, Chaos and Hopf bifurcation of a finance system, Nonlinear Dyn. 58 (2009), 58 (2009), 209.  doi: 10.1007/s11071-009-9472-5.  Google Scholar

[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), 67 (2012), 2171.  doi: 10.1007/s11071-011-0137-9.  Google Scholar

[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), 8 (2009), 59.   Google Scholar

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