Bi-center conditions and local bifurcation of critical periods in a switching Z2 equivariant cubic system

In this study, we consider bi-centers and local bifurcation of critical periods for a switching Z2 equivariant cubic system. We give the necessary and sufficient conditions for the system to have bi-centers at the symmetrical singular points ( ± 1, 0). We develop a method for computing the period constants near the center of switching systems and use this method to study bifurcation of critical periods for a switching system. We further find the existence of 10 local critical periods bifurcating from these bi-centers.