Skip to main content
SpringerLink
Log in

Effect of rectified and modulated sine forces on chaos in Duffing oscillator

  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

The effect of rectified and modulated sine forces on the onset of horseshoe chaos is studied both analytically and numerically in the Duffing oscillator. With single force analytical threshold condition for the onset of horseshoe chaos is obtained using the Melnikov method. The Melnikov threshold curve is drawn in a parameter space. For the rectified sine wave, onset of cross-well asymptotic chaos is observed just above the Melnikov threshold curve. For the modulus of sine wave long time transient motion followed by a periodic attractor is realized. The possibility of controlling of chaos by the addition of second modulated force is then analyzed. Parametric regimes where suppression of horseshoe chaos occurs are predicted analytically and verified numerically. Interestingly, suppression of chaos is found in the parametric regimes where the Melnikov function does not change sign.

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. R Chacon Control of Homoclinic Chaos by Weak Periodic Perturbations (Singapore: World Scientific) (2005)

    MATH  Google Scholar 

  2. K Konishi Phys. Lett. A320 200 (2003)

    MathSciNet  ADS  Google Scholar 

  3. A Y T Leung and L Zengrong Int. J. Bifur. Chaos 14 1455 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Z M Ge and W Y Leu Chaos, Solitons and Fractals 20 503 (2004)

    Article  MATH  Google Scholar 

  5. Y C Lai, Z Liu, A Nachman and L Zhu Int. J. Bifur. Chaos 14 3519 (2004)

    Article  MATH  Google Scholar 

  6. VM Gandhimathi, S Rajasekar and J Kurths Int. J. Bifur. Chaos 18 2073 (2008)

    Article  Google Scholar 

  7. B R Nana Nbendjo, Y Salissou and P Woafo Chaos, Solitons and Fractals 23 809 (2005)

    Article  MATH  Google Scholar 

  8. Y Tang, F Yang, G Chen and T Zhou Chaos, Solitons and Fractals 28 76 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. R Wang, J Deng and Z Jing Chaos, Solitons and Fractals 27 249 (2006)

    Article  MathSciNet  Google Scholar 

  10. F Balibrea, R Chacon and M A Lopez Chaos, Solitons and Fractals 24 459 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. X Wang, Y C Lai and C H Lai Chaos 16 023127 (2006)

    Article  ADS  Google Scholar 

  12. J Yang, W Feng and Z Jing Chaos, Solitons and Fractals 30 235 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  13. Z Jing, Z Yang and T Jiang Chaos, Solitons and Fractals 27 722 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  14. H Gao and G Chen Int. J. Bifur. Chaos 15 2411 (2005)

    Article  Google Scholar 

  15. J Guckenheimer and P Holmes Dynamical Systems and Bifurcations of Vector Fields (New York: Springer) (1990)

    Google Scholar 

  16. S Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos (New York: Springer) (1990)

    MATH  Google Scholar 

  17. S Zambrano, E Allaria, S Brugioni, I Leyva, R Meucci, M A F Sanjuan and F TArecchi Chaos 16 013111 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Sri K G S Arts College, Srivaikuntam, 628 619, Tamilnadu, India

    V. Ravichandran & V. Chinnathambi

  2. Bharathidasan University, Tiruchirapalli, 620 024, Tamilnadu, India

    S. Rajasekar

Authors
  1. V. Ravichandran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Chinnathambi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Rajasekar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Rajasekar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ravichandran, V., Chinnathambi, V. & Rajasekar, S. Effect of rectified and modulated sine forces on chaos in Duffing oscillator. Indian J Phys 83, 1593–1603 (2009). https://doi.org/10.1007/s12648-009-0143-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-009-0143-7

Keywords

Search

Navigation