Skip to main content
SpringerLink
Log in

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

  • Published:
Science in China Series G: Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pecora L M, Carroll T L. Synchronization in chaotic systems. Phys Rev Lett, 1990, 64(8): 821–824

    Article  ADS  MathSciNet  Google Scholar 

  2. Wang H J, Huang H B, Qi G X. Long-time anticipation of chaotic states in time-delay coupled ring and linear arrays. Phys Rev E, 2005, 71(1): 15202–15205

    Article  Google Scholar 

  3. Lü L, Luan L, Guo Z A. Synchronization of chaotic systems of different orders. Chin Phys, 2007, 16(2): 346–351

    Article  ADS  Google Scholar 

  4. Lü L, Guo Z A, Zhang C. Synchronization between two different chaotic systems with nonlinear feedback control. Chin Phys, 2007, 16(6): 1603–1607

    Article  ADS  Google Scholar 

  5. Yassen M T. Controlling, synchronization and tracking chaotic Liu system using active backstepping design. Phys Lett A, 2007, 360(4–5): 582–587

    Article  ADS  Google Scholar 

  6. Haken H. Synchronization and pattern recognition in a pulse-coupled neural net. Phys D, 2005, 205(1–4): 1–6

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Ge Z M, Chang C M, Chen Y S. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems. Chaos Solit Fract, 2006, 27(5): 1298–1315

    Article  MATH  Google Scholar 

  8. Tsimring L S, Rulkov N F, Larsen M L, et al. Repulsive synchronization in an array of phase oscillators. Phys Rev Lett, 2005, 95(1): 14101–14104

    Article  ADS  Google Scholar 

  9. Wang Y W, Guan Z H, Wang H O. Impulsive synchronization for Takagi-Sugeno fuzzy model and its application to continuous chaotic system. Phys Lett A, 2005, 339 (3–5): 325–332

    Article  ADS  Google Scholar 

  10. Deng X L, Huang H B. Spatial periodic synchronization of chaos in coupled ring and linear arrays of chaotic systems. Phys Rev E, 2002, 65(5): 55202–55204

    Article  ADS  Google Scholar 

  11. Kocarev L, Parlitz U, Brown R. Robust synchronization of chaotic systems. Phys Rev E, 2000, 61(4): 3716–3720

    Article  ADS  Google Scholar 

  12. Zou Y L, Zhu J. Controlling projective synchronization in coupled chaotic systems. Chin Phys, 2006, 15(9): 1965–1970

    Article  ADS  Google Scholar 

  13. Lu W L, Chen T P. New approach to synchronization analysis of linearly coupled ordinary differential systems. Phys D, 2006, 213(2): 214–230

    Article  MATH  MathSciNet  Google Scholar 

  14. Huang L, Feng R, Wang M. Synchronization of chaotic systems via nonlinear control. Phys Lett A, 2004, 320(4): 271–275

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Lü J H, Zhou T S, Zhang S C. Chaos synchronization between linearly coupled chaotic system. Chaos Solit Fract, 2002, 14(4): 529–541

    Article  MATH  Google Scholar 

  16. Lü J H, Chen G R. A new chaotic attractor coined. J Bifurc Chaos, 2002, 12(3): 659–661

    Article  MATH  Google Scholar 

  17. Zhou J, Lu J A, Lü J H. Adaptive synchronization of an uncertain complex dynamical network. IEEE Trans Autom Control, 2006, 51(4): 652–656

    Article  Google Scholar 

  18. Chen S H, Lü J H. Synchronization of an uncertain unified chaotic system via adaptive control. Chaos Solit Fract, 2002, 14(4): 643–647

    Article  MATH  Google Scholar 

  19. Lü J H, Chen G R, Cheng D Z, et al. Bridge the gap between the Lorenz system and the Chen system. J Bifurc Chaos, 2002, 12(12): 2917–2926

    Article  MATH  Google Scholar 

  20. Park J H. Adaptive synchronization of hyperchaotic Chen system with uncertain parameters. Chaos Solit Fract, 2005, 26(3): 959–964

    Article  MATH  Google Scholar 

  21. Kim J H, Park C W, Kim E, et al. Fuzzy adaptive synchronization of uncertain chaotic systems. Phys Lett A, 2005, 334(4): 295–305

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Pearson J E. Complex patters in a simple system. Science, 1993, 261(2): 189–192

    Article  ADS  MathSciNet  Google Scholar 

  23. Furuta K. Sliding mode control of a discrete system. Syst Contr Lett, 1990, 14(2): 145–152

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Physics and Electronic Technology, Liaoning Normal University, Dalian, 116029, China

    Ling Lü & Yi Li

  2. Department of Mathematics and Physics, Dalian Jiaotong University, Dalian, 116028, China

    ZhiAn Guo

Authors
  1. Ling Lü
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ZhiAn Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ling Lü.

Additional information

Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lü, L., Li, Y. & Guo, Z. Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system. Sci. China Ser. G-Phys. Mech. Astron. 51, 1638–1646 (2008). https://doi.org/10.1007/s11433-008-0162-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-008-0162-y

Keywords

Search

Navigation