Topological classifications of a piecewise linear Liénard system with three zones

Llibre et al. in [J. Nonlinear Sci., 2019] studied the number of limit cycles of piecewise linear Liénard system with one anti-saddle at the central zone in some parameter regions. However, the exact number and hyperbolicity of limit cycles were still unclear as in these cases of parameter. The goal of this paper is to give the exact number of limit cycles and the hyperbolicity of limit cycles in these parameter cases, where the maximum number of limit cycles is two. Moreover, all corresponding global phase portraits in the Poincaré disc are obtained.