Skip to main content
SpringerLink
Log in

Generating Lorenz-like and Chen-like attractors from a simple algebraic structure

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

This paper reports the finding of a very simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. Its algebraic structure is simple with only four linear terms and two quadratic terms. The quadratic terms are different from the Lorenz and the Chen systems. However, by tuning the only parameter, this new family of systems can also generate both Lorenz-like and Chen-like attractors, thus further reveal the close relation between them.

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. Lorenz E N. Deterministic nonperiodic flow. J Atmos Sci, 1963, 20: 130–141

    Article  Google Scholar 

  2. Chen G, Ueta T. Yet another chaotic attractor. Int J Bifur Chaos, 1999, 9: 1465–1466

    Article  MATH  MathSciNet  Google Scholar 

  3. Ueta T, Chen G. Bifurcation analysis of chen’s equation. Int J Bifur Chaos, 2000, 10: 1917–1931

    MATH  MathSciNet  Google Scholar 

  4. Zhou T, Tang Y, Chen G. Chen’s attractor exists. Int J Bifur Chaos, 2004, 14: 3167–3177

    Article  MATH  MathSciNet  Google Scholar 

  5. Zhou T, Tang Y, Chen G. Complex dynamical behaviors of the chaotic chen’s system. Int J Bifur Chaos, 2003, 13: 2561–2574

    Article  MATH  MathSciNet  Google Scholar 

  6. Lü J, Chen G, Cheng D, et al. Bridge the gap between the Lorenz system and the Chen system. Int J Bifur Chaos, 2002, 12: 2917–2926

    Article  MATH  Google Scholar 

  7. Čelikovský S, Vanečěk A. Bilinear systems and chaos. Kybernetika, 1994, 30: 403–424

    MATH  MathSciNet  Google Scholar 

  8. Čelikovský S, Chen G. On a generalized lorenz canonical form of chaotic systems. Int J Bifur Chaos, 2002, 12: 1789–1812

    Article  MATH  Google Scholar 

  9. Čelikovský S, Chen G. Hyperbolic-type generalized Lorenz system and its canonical form. In: Proceedings of the 15th Triennial World Congress of IFAC, Barcelona, 2002

    Google Scholar 

  10. Čelikovský S, Chen G. On the generalized lorenz canonical form. Chaos Solit Fract, 2005, 26: 1271–1276

    Article  MATH  Google Scholar 

  11. Wang X, Chen J, Lu J A, et al. A simple yet complex one-parameter family of generalized Lorenz-like systems. Int J Bifur Chaos, 2012, 22: 1250116

    Article  MathSciNet  Google Scholar 

  12. Lü J, Zhou T. The compound structure of Chens attractor. Int J Bifur Chaos, 2002, 12: 855–858

    Article  MATH  Google Scholar 

  13. Yang Q, Chen G. A chaotic system with one saddle and two stable node-foci. Int J Bifur Chaos, 2008, 18: 1393–1414

    Article  MATH  Google Scholar 

  14. Chen G, Lü J. Dynamics of the Lorenz System Family: Analysis, Control and Synchronization (in Chinese). Beijing: Science Press, 2003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China

    Xiong Wang & GuanRong Chen

Authors
  1. Xiong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GuanRong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiong Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Chen, G. Generating Lorenz-like and Chen-like attractors from a simple algebraic structure. Sci. China Inf. Sci. 57, 1–7 (2014). https://doi.org/10.1007/s11432-013-4932-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-013-4932-4

Keywords

Search

Navigation