Abstract
We investigate nonsmooth planar systems of differential equations with discontinuous right-hand side. Discontinuity sets intersect at a vertex and are of the quasilinear nature. By means of the B-equivalence method, which was introduced in Akhmet and Kashkynbayev (Proceedings of 10th QTDE, Electronic Journal of Qualitative Theory of Differential Equations, 2016, [46], Akhmetov and Perestyuk (Ukr Math J 43:1209–1214, 1991, [54], Akhmet and Kashkynbayev (Nonautonomous Bifurcation in Hybrid Systems, submitted [55] (see also Akhmet, Principles of Discontinuous Dynamical Systems, 2010, [1], Akhmet, Nonlinear Anal: TMA 60:163–178, 2005, [6]), these systems are reduced to impulsive differential equations. Sufficient conditions are established for the existence of foci and centers both in the noncritical and critical cases. Hopf bifurcation is considered from a vertex, which unites several curves, in the critical case. An appropriate example is provided to illustrate the results.
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Akhmet, M., Kashkynbayev, A. (2017). Hopf Bifurcation in Filippov Systems. In: Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-10-3180-9_3
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DOI: https://doi.org/10.1007/978-981-10-3180-9_3
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Online ISBN: 978-981-10-3180-9
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