No abstract

Abstract. We study the Darboux and the analytic integrability of the Rucklidge system.

We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones.

No abstract

In this paper we consider a class of planar continuous piecewise linear vector fields with three zones. Using the Poincaré map we show that these systems admit always a unique limit cycle, which is hyperbolic.