Degenerate grazing-sliding bifurcations in planar Filippov systems
This paper studies a class of degenerate grazing-sliding bifurcations of piecewise planar differential systems, whose unperturbed system has a generalized homoclinic loop to a fold-fold point. According to differential types of fold-fold points, the authors exhibit some codimension-2 bifurcation diagrams together with the asymptotics of all bifurcation curves. This work reveals several complete unfoldings of degenerate grazing-sliding bifurcations. As a consequence, they answer the problem posed in [\textit{F. Liang} et al., ibid. 255, No. 12, 4403--4436 (2013; Zbl 1301.34055)] on the maximum number of limit cycles bifurcating from the generalized homoclinic loop in case of fold-fold point.
scientific article; zbMATH DE number 7260140
scientific article