On the Heteroclinic Connections in the 1 : 3 Resonance Problem

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

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Detail(s)

Original languageEnglish
Article number1650143
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume26
Issue number8
StatePublished - 1 Jul 2016

Abstract

Analytical predictions of the triangle and clover heteroclinic bifurcations in the problem of self-oscillations stability loss near 1:3 resonance are provided using the method of nonlinear time transformation. The analysis was carried out considering the slow flow of a self-excited nonlinear Mathieu oscillator corresponding to the normal form near this 1:3 strong resonance. Using the Hamiltonian system of the corresponding slow flow near this resonance, the unperturbed zero-order approximation of the heteroclinic connections is established. Conditions of persistence of homoclinic connections in the perturbed first-order approximation of the heteroclinic connections provide close analytical approximations of the triangle and clover heteroclinic bifurcation curves, simultaneously. The analytical predictions are compared to the results obtained by numerical simulations for validation.

Research Area(s)

  • 1:3 resonance, heteroclinic bifurcation, nonlinear time transformation, perturbation analysis, self-oscillations

Citation Format(s)

On the Heteroclinic Connections in the 1 : 3 Resonance Problem. / Qin, B. W.; Chung, K. W.; Fahsi, A.; Belhaq, M.

In: International Journal of Bifurcation and Chaos, Vol. 26, No. 8, 1650143, 01.07.2016.

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