Heteroclinic connections in the 1 : 4 resonance problem using nonlinear transformation method

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)2479-2486
Journal / PublicationNonlinear Dynamics
Volume78
Issue number4
Online published3 Aug 2014
Publication statusPublished - Dec 2014

Abstract

In this paper, the method of nonlinear time transformation is applied to obtain analytical approximation of heteroclinic connections in the problem of stability loss of self-oscillations near 1:4 resonance. As example, we consider the case of parametric and self-excited oscillator near the 1:4 subharmonic resonance. The method uses the unperturbed heteroclinic connection in the slow flow to determine conditions under which the perturbed heteroclinic connection persists. The results show that for small values of damping, the nonlinear time transformation method can predict well both the square and clover heteroclinic connection near the 1:4 resonance. The analytical finding is confirmed by comparisons to the results obtained by numerical simulations.

Research Area(s)

  • 1:4 Resonance, Heteroclinic bifurcation, Nonlinear transformation, Perturbation analysis

Citation Format(s)

Heteroclinic connections in the 1 : 4 resonance problem using nonlinear transformation method. / Chung, K. W.; Cao, Y. Y.; Fahsi, A. et al.

In: Nonlinear Dynamics, Vol. 78, No. 4, 12.2014, p. 2479-2486.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review