Resumen de Coexistence of Analytic and Piecewise Analytic Limit Cycles in Planar Piecewise Quadratic Differential Systems

Leonardo Pereira Costa da Cruz, Alex C. Rezende, Joan Torregrosa Arús

• We study the simultaneous bifurcation of limit cycles in planar piecewise quadratic differential systems separated by a straight line. These limit cycles arise from a degenerate Hopf bifurcation at two equilibrium points in the positive and negative half-planes, as well as from an equilibrium on the separation line. All the limit cycles are of small amplitude. This bifurcation creates a configuration of limit cycles of type (3, 5, 3).

  Additionally, in each half-plane, the maximum number of small-amplitude hyperbolic limit cycles that a quadratic vector field can have is three.