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

Ravichandran, V.; Chinnathambi, V.; Rajasekar, S.

doi:10.1007/s12648-009-0143-7

Cited by 5 publications

(2 citation statements)

References 16 publications

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“…For instance, addition of constant bias [4][5][6], quadratic nonlinear term x 2 [4,[7][8][9], variable shape parametric perturbation [10,11], replacing cubic nonlinearity by the quadratic nonlinear term [12][13][14] and asymmetrical periodic driving force [15] have physical significance and represent real physical systems in different disciplines. In the presence of such symmetry breaking perturbations, the occurrence of homoclinic bifurcation, structure of strange attractors, hysteresis jump, routes to chaos, basin boundary structure and escape dynamics have been investigated in the Duffing oscillator.…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of such symmetry breaking perturbations, the occurrence of homoclinic bifurcation, structure of strange attractors, hysteresis jump, routes to chaos, basin boundary structure and escape dynamics have been investigated in the Duffing oscillator. In addition, the effect of variable shape forces [16,17], different types of periodic forces [15] and nonlinear damping [18,19] have also been analysed.…”

Section: Introductionmentioning

confidence: 99%

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Role of asymmetries in the chaotic dynamics of the double-well Duffing oscillator

Ravichandran¹,

Jeyakumari²,

Chinnathambi³

et al. 2009

Pramana - J Phys

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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.

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