Abstract
The main objective of this paper is to study bifurcations of a vector field in a neighborhood of a cycle having a homoclinic-like connection at a saddle-regular point. In order to perform such a study it is necessary to analyze how the cycle can be broken, in this way the approach is to look separately at local bifurcations and at the structure of the first return map defined near the cycle.
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References
A.F. Filippov, Differential Equations with Discontinuous Right-Hand Sides, vol. 18, Mathematics and its Applications (Kluwer Academic Publishers Group, Dordrecht, 1988)
M. Guardia, T.M. Seara, M.A. Teixeira, Generic bifurcations of low codimension of planar Filippov systems. J. Differ. Equ. 250, 1967–2023 (2011)
Y.A. Kuznetsov, S. Rinaldi, A. Gragnani, One-parameter bifurcations in planar Filippov systems. Int. J. Bifurc. Chaos Appl. Sci. Eng. 13(8), 2157–2188 (2003)
R. Roussarie, Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem (Birkhuser, Basel, 1998)
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da S. Andrade, K., Martins, R.M., Teixeira, M.A. (2017). On Degenerate Cycles in Planar Filippov Systems. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_1
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DOI: https://doi.org/10.1007/978-3-319-55642-0_1
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