Limit cycles of piecewise smooth differential systems with nilpotent center and linear saddle

Abstract

In this paper, we study the number of limit cycles of a piecewise smooth differential system separated by one or two parallel straight lines or rays formed by a nilpotent center or degenerate center and linear saddle. Piecewise linear differential systems separated by one or two parallel straight lines with one of the subsystems of type nilpotent center and other subsystems of type linear saddle can have at most two limit cycles and there are systems in these classes having one limit cycle. The limit cycle in particular consists of saddle separatrices of the subsystem.