Skip to main content
SpringerLink
Log in

Observation of chaos in a nonlinear oscillator with delay: A numerical study

  • Published:
KSME Journal Aims and scope Submit manuscript

Abstract

The Van der Pol-Duffing's oscillator with time delay is investigated. Some examples of the different behaviour of strange attractors with the changing of delay parameters are given. For certain parameter values the motion of the oscillator is harmonic with only one frequency.

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

  • Awrejcewicz, J., in press, “A Route to Chaos in a Nonlinear Oscillator with Delay”, Acta Mechanica.

  • Awrejcewicz, J. and Barron, R., 1988, “Chaotic Motion of a Cylindrical Container on a Non-Linear Suspension: Experimental Results”, Journal of Sound and Vibration 121(3), pp. 563–566.

    Article  Google Scholar 

  • Grebogi, C., Ott, E., Pelikan, S. and Yorke, J.A., 1984, “Strange Attractors that are not Chaotic”, Physica 130, 261–268.

    MathSciNet  Google Scholar 

  • Grebogi, C., Ott, E. and Yorke, J.A., 1988, “Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics”, Science v. 238, pp. 632–638.

    MathSciNet  Google Scholar 

  • Hayashi, C., 1964, “Nonlinear Oscillations in Physical Systems, McGraw Hill.

  • Holden, A.V., 1986, “Chaos”, Manchester University Press.

  • Holmes, P., 1979, “A Nonlinear Oscillator with the Strange Attractor”, Philosophical Transactions of the Royal Society 292A, pp. 419–448.

    Google Scholar 

  • Holmes, P.J. and Moon, F.C., 1983, “Strange Attractors and Chaos in Nonlinear Mechanics,” Journal of Applied Mechanics 50, 1021–1032.

    MathSciNet  Google Scholar 

  • Lorenz, E.N., 1963, “Deterministic Non-Periodic Flow”, Journal of Atmospheric Science 20, pp. 130–141.

    Article  Google Scholar 

  • Minorsky, N., 1962, “Nonlinear Oscillations”, Van Nostrand. London.

    MATH  Google Scholar 

  • Plaut, R.H. and Hsieh, J.-C., 1987, “Chaos in a Mechanism with Time Delays under Parametric and External Excitation”, Journal of Sound and Vibration 114(1), pp. 73–90.

    Article  MathSciNet  Google Scholar 

  • Sparrow, C., 1982, “Bifurcation, Chaos and Strange Attractors,” Applied Mathematical Sciences 41, Springer: New York, Heidelberg, Berlin.

    Google Scholar 

  • Ueda, Y., 1979, “Randomly Transitional Phenomena in the System Governed by Duffing's Equation”, Journal of Statistical Physics 20, pp. 181–186.

    Article  MathSciNet  Google Scholar 

  • Ueda, Y. and Akamatsu, N., 1981, “Chaotically Transitional Phenomena in the Forced Resistance Oscillator”, Institute of Electrical and Electronic Engineers Transaction on Circuit and Systems CAS-28. pp. 217–223.

Download references

Author information

Authors and Affiliations

  1. Institute of Technical Mechanics, Technical University, Spiel mannstrasse 11, 3300, Braunschweig, West Germany

    J. Awrejcewicz

  2. Institute of Applied Mechanics, Technical University, Stefanowskiego 1/15, 90-924, Lodz, Poland

    J. Wojewoda

Authors
  1. J. Awrejcewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Wojewoda
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Awrejcewicz, J., Wojewoda, J. Observation of chaos in a nonlinear oscillator with delay: A numerical study. KSME Journal 3, 15–24 (1989). https://doi.org/10.1007/BF02945679

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02945679

Key Words

Search

Navigation