Advertisement

Pramana

, 92:42 | Cite as

A complete analytical study on the dynamics of simple chaotic systems

  • G Sivaganesh
  • A ArulgnanamEmail author
  • A N Seethalakshmi
Article
First Online:
  • 6 Downloads

Abstract

We report, in this paper, a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical solutions revealing several chaotic phenomena such as antimonotonicity, period-doubling sequences and Feignbaum remerging have been presented. Further, the analytical solutions are used to obtain basins of attraction, phase portraits and Poincare maps for different chaotic systems. Experimentally observed chaotic attractors in some of the systems are presented to confirm the analytical results. The bifurcations and chaotic phenomena studied through explicit analytical solutions are reported in the literature for the first time.

Keywords

Chaos antimonotonicity piecewise linear 

PACS Nos

05.45.−a 05.45.Ac 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

One of the authors A Arulgnanam gratefully acknowledges Dr K Thamilmaran, the Centre for Nonlinear Dynamics, Bharathidasan University, Tiruchirapalli, for his help and permission to carry out the experimental work during his doctoral programme.

References

  1. 1.
    M J Ogorzalek, IEEE Trans. Circuits Syst. I  4 0, 693 (1993)CrossRefGoogle Scholar
  2. 2.
    M Lakshmanan and K Murali, Curr. Sci.  67, 989 (1994)Google Scholar
  3. 3.
    M Lakshmanan and S Rajasekar, Nonlinear dynamics: Integrability, chaos and patterns (Springer, Berlin, 2003)Google Scholar
  4. 4.
    T Matsumoto, IEEE Trans. Circuits Syst.  31, 1055 (1984)Google Scholar
  5. 5.
    K Murali, M Lakshmanan and L O Chua, IEEE Trans. Circuits Syst.  41, 462 (1994)Google Scholar
  6. 6.
    A Arulgnanam, K Thamilmaran and M Daniel, Chaos Solitons Fractals  42, 2246 (2009)ADSCrossRefGoogle Scholar
  7. 7.
    K Thamilmaran, M Lakshmanan and K Murali, Int. J. Bifurc. Chaos  10, 1175 (2000)CrossRefGoogle Scholar
  8. 8.
    A Arulgnanam, K Thamilmaran and M Daniel, Chin. J. Phys.  53, 060702 (2015)Google Scholar
  9. 9.
    B C Lai and J J He, Pramana – J. Phys.  90: 33 (2018)ADSCrossRefGoogle Scholar
  10. 10.
    P M Ezhilarasu, M Inbavalli, K Murali and K Thamilmaran, Pramana – J. Phys.  91: 4 (2018)ADSCrossRefGoogle Scholar
  11. 11.
    M P Kennedy, Frequenz  46, 66 (1992)ADSCrossRefGoogle Scholar
  12. 12.
    J G Lacy, Int. J. Bifurc. Chaos  6, 2097 (1996)CrossRefGoogle Scholar
  13. 13.
    M Lakshmanan and K Murali, Phil. Trans: Phys. Sci. Eng.  353, 1701 (1995)Google Scholar
  14. 14.
    G Sivaganesh, Chin. J. Phys.  52, 1760 (2014)MathSciNetGoogle Scholar
  15. 15.
    G Sivaganesh and A Arulgnanam, J. Korean Phys. Soc.  69, 1631 (2016)ADSCrossRefGoogle Scholar
  16. 16.
    K Thamilmaran and M Lakshmanan, Int. J. Bifurc. Chaos  12, 783 (2001)CrossRefGoogle Scholar
  17. 17.
    G Sivaganesh, Chin. Phys. Lett.  32, 010503 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    P R Venkatesh, A Venkatesan and M Lakshmanan, Pramana – J. Phys.  86, 1195 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    G Sivaganesh and A Arulgnanam, Chin. Phys. B  26(5), 050502 (2017)ADSCrossRefGoogle Scholar
  20. 20.
    G Sivaganesh, A Arulgnanam and A N Seethalakshmi, Chaos Solitons Fractals  113, 294 (2018)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of PhysicsAlagappa Chettiar Government College of Engineering and TechnologyKaraikudiIndia
  2. 2.Department of Physics, St. John’s College (affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, India)PalayamkottaiIndia
  3. 3.Department of Physics, The M.D.T. Hindu College (affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli 627 012, India)TirunelveliIndia

Personalised recommendations