Abstract
We study the dynamics of a continuous planar piecewise linear differential system with three zones separated by two parallel lines. We provide a complete study on the maximum number of limit cycles by geometric techniques when the system is degenerate in the left and central zones. The bifurcation diagrams and global phase portraits in the Poincaré disc are given. It is shown that a degenerate continuous planar piecewise linear differential system can have scabbard bifurcation, grazing bifurcation and double limit cycle bifurcation. Moreover, we detect three new scabbard bifurcations, such as both the limit cycle with two zones and the limit cycle with three zones can be bifurcated from a singular continuum with infinite length.
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