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 › peer-review
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Detail(s)
Original language | English |
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Article number | 1650143 |
Journal / Publication | International Journal of Bifurcation and Chaos |
Volume | 26 |
Issue number | 8 |
Publication status | Published - Jul 2016 |
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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, 07.2016.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review