Limit Cycles in a Class of Continuous–Discontinuous Piecewise Linear Differential Systems with Three Zones

In this paper, we investigate the existence of limit cycles in piecewise linear systems separated by two parallel straight lines, where in one of these straight lines, the piecewise differential system is continuous, and in the other, it is discontinuous. Based on the methods of Poincaré map and first integral, we prove that these systems can have at most two limit cycles. Additionally, taking into account the type of singular points in the zones, we present examples with one or two limit cycles for all possible combinations.