Center and isochronous center conditions for switching systems associated with elementary singular points

• Present a computationally efficient method for computing the focal values and periodic constants of switching systems.
• Prove that a cubic switching system can have at least 15 limit cycles. This is a new best result obtained so far for cubic switching systems.
• The methodology can be directly applied to study high-order switching systems or generalized to consider other types of discontinuous systems.

In this paper, an existing method is modified for computing the focal values and period constants of switching systems associated with elementary singular points. In particular, a quadratic switching system is considered to illustrate the computational efficiency of this method. Further, with this method, a cubic switching system is constructed to show existence of 15 limit cycles, which is the best result so far obtained for cubic switching systems.