Abstract:

We will study the algebraic limit cycles of planar piecewise linear differential systems. In particular we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some 1-parameter families with a saddle-node bifurcation of algebraic limit cycles. We also show that all degrees for algebraic limit cycles are allowed. This is a joint work with Claudio Buzzi and Armengol Gasull. The paper has been accepted for publication in International Journal of Bifurcation and Chaos.