Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems

Akhmet, 2005, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Anal., 60, 163, 10.1016/j.na.2004.08.029 Akhmet, 2009, Bifurcation of a non-smooth planar limit cycle from a vertex, Nonlinear Anal., 71, 2723, 10.1016/j.na.2009.06.031 Banerjee, 2001 Bernardo, 2003, Sliding bifurcations: a novel mechanism for the sudden onset of chaos in dry friction oscillators, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13, 2935, 10.1142/S021812740300834X Coll, 2001, Degenerate Hopf bifurcation in discontinuous planar systems, J. Math. Anal. Appl., 253, 671, 10.1006/jmaa.2000.7188 Dankowicz, 2000, On the origin and bifurcations of stick-slip oscillators, Physica D, 136, 280, 10.1016/S0167-2789(99)00161-X Filippov, 1988, Differential Equations with Discontinuous Righthand Side, 10.1007/978-94-015-7793-9 Freire, 1997, Hopf-like bifurcations in planar piecewise systems, Publ. Mat., 41, 135, 10.5565/PUBLMAT_41197_08 Giannakopoulos, 2001, Planar systems of piecewise linear differential equations with a line of discontinuity, Nonlinearity, 14, 1611, 10.1088/0951-7715/14/6/311 Guardia, 2011, Generic bifurcations of low codimension of planar Filippov systems, J. Differential Equations, 250, 1967, 10.1016/j.jde.2010.11.016 Hale, 1980 Han, 2010, On Hopf bifurcation in non-smooth planar system, J. Differential Equations, 248, 2399, 10.1016/j.jde.2009.10.002 Kukučka, 2007, Melnikov method for discontinuous planar systems, Nonlinear Anal., 66, 2698, 10.1016/j.na.2006.04.001 Kunze, 2000, Non-smooth Dynamical Systems, 10.1007/BFb0103843 Küpper, 2001, Generalized Hopf bifurcation for non-smooth planar systems, Philos. Trans. R. Soc. Lond. A, 359, 2483, 10.1098/rsta.2001.0905 Kuznetsov, 2003, One-parameter bifurcations in planar Filippov systems, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13, 2157, 10.1142/S0218127403007874 Leine, 2000 Leine, 2006, Bifurcations of equilibria in non-smooth continuous systems, Physica D, 223, 121, 10.1016/j.physd.2006.08.021 Leine, 2004, Dynamics and Bifurcations of Nonsmooth Mechanical Systems Liberzon, 2003 Shui, 2010, The qualitative analysis of a class of planar Filippov systems, Nonlinear Anal., 73, 1277, 10.1016/j.na.2010.04.053 Zhusubalyev, 2003 Zou, 2006, Generalized Hopf bifurcation for planar Filippov systems continuous at the origin, J. Nonlinear Sci., 16, 159, 10.1007/s00332-005-0606-8