Abstract
Duffing oscillator driven by a periodic force with three different forms of asymmetrical double-well potentials is considered. Three forms of asymmetry are introduced by varying the depth of the left-well alone, location of the minimum of the left-well alone and above both the potentials. Applying the Melnikov method, the threshold condition for the occurrence of horseshoe chaos is obtained. The parameter space has regions where transverse intersections of stable and unstable parts of left-well homoclinic orbits alone and right-well orbits alone occur which are not found in the symmetrical system. The analytical predictions are verified by numerical simulation. For a certain range of values of the control parameters there is no attractor in the left-well or in the right-well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M Lakshmanan and S Rajasekar, Nonlinear dynamics: Integrability, chaos and patterns (Springer, Berlin, 2003)
E Simiu, Chaotic transitions in deterministic and stochastic dynamical systems (Princeton University Press, New Jersey, 2002)
V Ravichandran, V Chinnathambi and S Rajasekar, Phys. A376, 223 (2007) and references therein
R Räty, J von Boehm and H M Isomaki, Phys. Rev. A34, 4310 (1986)
G Cicogna and F Papoff, Europhys. Lett. 3, 963 (1987)
M Arrayas, M I Dykman, R Mannella, P V E McClintock and N D Stein, Phys. Rev. Lett. 84, 5470 (2000)
S Lenci and G Rega, Nonlin. Dyn. 33, 71 (2003)
S Lenci and G Rega, Chaos, Solitons and Fractals 21, 1031 (2004)
H Cao, J M Seoane and M A F Sanjuán, Chaos, Solitons and Fractals 34, 197 (2007)
F Balibrea, R Chacon and M A Lopez, Chaos, Solitons and Fractals 24, 459 (2005)
A Litvak-Hinenzon and V Rom-Kedar, Phys. Rev. E55, 4964 (1997)
C S Wang, Y H Kao, J C Huang and Y S Gou, Phys. Rev. A45, 3471 (1992)
J A Almendral, J Seoane and M A F Sanjuán, Recent Res. Devel. Sound Vib. 2, 115 (2004)
J A Almendral and M A F Sanjuán, J. Phys. A36, 695 (2003)
V Ravichandran, V Chinnathambi and S Rajasekar (2009) submitted for publication
R Chacon, Phys. Rev. E54, 6153 (1996)
R Chacon and J D Bejarno, Phys. Rev. Lett. 71, 3103 (1993)
M A F Sanjuán, Int. J. Bifurcat. Chaos 9, 735 (1999)
M S Siewe, H Cao and M A F Sanjuán, Chaos, Solitons and Fractals (2009), in press
J Guckenheimer and P Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields (Springer, New York, 1983)
K Chun and N O Birge, Phys. Rev. B48, 11500 (1993)
N M Zimmerman et al, Phys. Rev. Lett. 67, 1322 (1991)
R Lofstedt and S N Coppersmith, Phys. Rev. Lett. 72, 1947 (1994)
S Wiggins, Introduction to applied nonlinear dynamical systems and chaos (Springer, New York, 1990)
M S Siewe and F M Moukam Kakmeni, C Tchawoua and W Woafo, Physica A357, 383 (2005)
Z Jing, Z Yang and T Jiang, Chaos, Solitons and Fractals 27, 722 (2006)
R Bourkha and M Belhaq, Chaos, Solitons and Fractals 34, 621 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ravichandran, V., Jeyakumari, S., Chinnathambi, V. et al. Role of asymmetries in the chaotic dynamics of the double-well Duffing oscillator. Pramana - J Phys 72, 927–937 (2009). https://doi.org/10.1007/s12043-009-0086-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-009-0086-8