Abstract
An analytical approach to predicting a critical parameter valueof homoclinic bifurcation in a three-dimensional system is reported. Themultiple scales method is first performed to construct a higher-orderapproximation of the periodic solution. A criterion based on a collisionbetween the periodic orbit and the fixed point involved in thebifurcation is applied. This criterion developed initially to predicthomoclinic bifurcations in planar autonomous systems, is adapted here toderive a critical value of the homoclinic bifurcation in a specificthree-dimensional system. To support our analytical predictions and todescribe the dynamical behaviour of the system, a complete numericalstudy is provided.
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Belhaq, M., Houssni, M., Freire, E. et al. Asymptotics of Homoclinic Bifurcation in a Three-Dimensional System. Nonlinear Dynamics 21, 135–155 (2000). https://doi.org/10.1023/A:1008353609572
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DOI: https://doi.org/10.1023/A:1008353609572