Skip to main content
SpringerLink
Log in

On properties of hyperchaos: Case study

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Some properties of hyperchaos are exploited by studying both uncoupled and coupled CML. In addition to usual properties of chaotic strange attractors, there are other interesting properties, such as: the number of unstable periodic points embedded in the strange attractor increases dramatically increasing and a large number of low-dimensional chaotic invariant sets are contained in the strange attractor. These properties may be useful for regarding the edge of chaos as the origin of complexity of dynamical systems.

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. Kaneko K. Pattern dynamics in spatiotemporal chaos.Physic D, 1989, 34: 1–41

    Article  MATH  MathSciNet  Google Scholar 

  2. Liu Zengrong, Huang Xin. A kind of dynamics with snap back repeller.Acta Mechanica Scinica, 1997, 29(1): 103–107 (in Chinese)

    Google Scholar 

  3. Marotto FR. Snap-back repellers imply chaos inR n.J Math Anal Appl, 1978, 63: 199–233

    Article  MATH  MathSciNet  Google Scholar 

  4. Marotto FR. Perturbation of stable and chaotic difference equation.J Math Anal Appl, 1979, 72: 716–729

    Article  MATH  MathSciNet  Google Scholar 

  5. Marotto FR. Chaotic behavior in the Henon mapping.Comm Math Phys, 1979, 68: 187–194

    Article  MATH  MathSciNet  Google Scholar 

  6. Liu Zengrong, Qin Wenxin, Xie Himin, Cao Yongluo. The structure of the stranges attractor of a kind of two-dimensional maps and dynamical behavior on it.Science in China A, 1993, 23(7): 702–708

    Google Scholar 

  7. Ott E, Grebogi C, Yorke JA. Controlling chaos.Phys Rev Lett, 1990, 64: 1196–1199

    Article  MATH  MathSciNet  Google Scholar 

  8. Yang Ling, Liu Zengrong. An improvement and proof of OGY method.Appl Math Mech, 1998, 19(1): 1–8

    Article  MathSciNet  Google Scholar 

  9. Chen Liqun, Liu Yanzhu. Control of the Lorenz chaos by the exact linearization.Appl Math Mech, 1998, 19(1): 67–73

    Article  MathSciNet  Google Scholar 

  10. Chen Liqun, Liu Yanzhu. Controlling chaos: present and future.J Shanghai Jiaotong Univ, 1998, 32(1): 108–114, (in Chinese)

    MathSciNet  Google Scholar 

  11. Waldrop MM. Complexity: The emerging science at the edge of order and chaos. Simon & Schuster, 1992

  12. Badii R, Politi A. Complexity: Hierarchical structures and scaling in physics. Cambridge, 1997

Download references

Author information

Authors and Affiliations

  1. LNM, The Institute of Mechanics, Academia Sinica, 100080, Beijing, China

    Liu Zengrong & Yang Ling

  2. Dept. of Math., Shanghai University, 201800, Shanghai, China

    Liu Zengrong, Chen Liqun & Yang Ling

Authors
  1. Liu Zengrong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Liqun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Ling
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The project supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zengrong, L., Liqun, C. & Ling, Y. On properties of hyperchaos: Case study. Acta Mech Sinica 15, 366–370 (1999). https://doi.org/10.1007/BF02487934

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02487934

Key Words

Search

Navigation