科研之友
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摘要
In this paper, we mainly discuss Hopf bifurcation for planar nonsmooth general systems and Lienard systems with foci of parabolic-parabolic (PP) or focus-parabolic (FP) type. For the bifurcation near a focus, when the focus is kept fixed under perturbations we prove that there are at most k limit cycles which can be produced from an elementary weak focus of order 2k + 2 (resp. k + 1)(k >= 1) if the focus is of PP (resp. FP) type, and we present the conditions to ensure these upper bounds are achievable. For the bifurcation near a center, the Hopf cyclicicy is studied for these systems. Some interesting applications are presented.
