American Institute of Mathematical Sciences

Advanced
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), 821-823. 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), 6627-2238. 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), 2607-2615. doi: 10.1016/j.nonrwa.2011.03.009.  Google Scholar

[4]

H. N. Agiza, Choas synchronization of Lüdynamical system Nonlinear Anal. 58 (2004), 11-20 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), 1457-1464 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), 662-669  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), 213-218 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), 231-237 doi: 10.1016/j.physleta.2006.08.092.  Google Scholar

[9]

D. Guégan, Chaos in economics and finance Annu Rev Control 33 (2009), 89-93 Google Scholar

[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.  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), 2171-2182 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), 59-66  Google Scholar

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.  Google Scholar

[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.  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), 2607-2615. doi: 10.1016/j.nonrwa.2011.03.009.  Google Scholar

[4]

H. N. Agiza, Choas synchronization of Lüdynamical system Nonlinear Anal. 58 (2004), 11-20 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), 1457-1464 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), 662-669  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), 213-218 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), 231-237 doi: 10.1016/j.physleta.2006.08.092.  Google Scholar

[9]

D. Guégan, Chaos in economics and finance Annu Rev Control 33 (2009), 89-93 Google Scholar

[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.  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), 2171-2182 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), 59-66  Google Scholar

[1]

Ruofeng Rao, Shouming Zhong. Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1375-1393. doi: 10.3934/dcdss.2020280
[2]

Rabiaa Ouahabi, Nasr-Eddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2361-2370. doi: 10.3934/dcdsb.2020182
[3]

István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete & Continuous Dynamical Systems, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773
[4]

Daniel Wilczak. Abundance of heteroclinic and homoclinic orbits for the hyperchaotic Rössler system. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 1039-1055. doi: 10.3934/dcdsb.2009.11.1039
[5]

Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete & Continuous Dynamical Systems, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079
[6]

Huijuan Li, Junxia Wang. Input-to-state stability of continuous-time systems via finite-time Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 841-857. doi: 10.3934/dcdsb.2019192
[7]

Hiroshi Ito. Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 5171-5196. doi: 10.3934/dcdsb.2020338
[8]

Catherine Lebiedzik. Uniform stability in a vectorial full Von Kármán thermoelastic system with solenoidal dissipation and free boundary conditions. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020092
[9]

Ming Mei, Yong Wang. Stability of stationary waves for full Euler-Poisson system in multi-dimensional space. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1775-1807. doi: 10.3934/cpaa.2012.11.1775
[10]

Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011
[11]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part II: The nonlinear system.. Evolution Equations & Control Theory, 2014, 3 (1) : 83-118. doi: 10.3934/eect.2014.3.83
[12]

Sébastien Court. Stabilization of a fluid-solid system, by the deformation of the self-propelled solid. Part I: The linearized system.. Evolution Equations & Control Theory, 2014, 3 (1) : 59-82. doi: 10.3934/eect.2014.3.59
[13]

Ruoxia Li, Huaiqin Wu, Xiaowei Zhang, Rong Yao. Adaptive projective synchronization of memristive neural networks with time-varying delays and stochastic perturbation. Mathematical Control & Related Fields, 2015, 5 (4) : 827-844. doi: 10.3934/mcrf.2015.5.827
[14]

Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443
[15]

Haijun Wang, Fumin Zhang. Bifurcations, ultimate boundedness and singular orbits in a unified hyperchaotic Lorenz-type system. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1791-1820. doi: 10.3934/dcdsb.2020003
[16]

Shin-Ichiro Ei, Kei Nishi, Yasumasa Nishiura, Takashi Teramoto. Annihilation of two interfaces in a hybrid system. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 857-869. doi: 10.3934/dcdss.2015.8.857
[17]

Yipeng Chen, Yicheng Liu, Xiao Wang. Exponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance. Evolution Equations & Control Theory, 2021  doi: 10.3934/eect.2021023
[18]

Luis Barreira, César Silva. Lyapunov exponents for continuous transformations and dimension theory. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 469-490. doi: 10.3934/dcds.2005.13.469
[19]

Carlos Arnoldo Morales, M. J. Pacifico. Lyapunov stability of $\omega$-limit sets. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 671-674. doi: 10.3934/dcds.2002.8.671
[20]

Luis Barreira, Claudia Valls. Stability of nonautonomous equations and Lyapunov functions. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2631-2650. doi: 10.3934/dcds.2013.33.2631

2019 Impact Factor: 1.27

Tools

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (10)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences