© 2016, Springer Science+Business Media Dordrecht. In this article, we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual. When the piecewise differential system is continuous, we show that the system has no limit cycles. But when the piecewise differential system is discontinuous, we show that it can have at most one limit cycle.
- Continuous piecewise linear differential systems
- Discontinuous piecewise differential systems
- Limit cycles