Hopf Cyclicity and Center Conditions for Some Piecewise Smooth Cubic Differential Systems

In this paper, we consider piecewise smooth differential systems with subsystems having cubic reversible isochronous centers at the origin, where the separation line is a straight line passing through the origin. By computing Lyapunov constants, we obtain Hopf cyclicity at the origin with necessary and sufficient conditions for the origin to be a center in this type of piecewise smooth differential systems.