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.

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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.

We present an algorithm which determines global conditions for a class of discontinuous vector fields in 4D (called polynomial relay systems) to have periodic orbits. We present explicit results relying on constructive proofs, which involve classical Effective Algebraic Geometry algorithms.

We study a class of quadratic reversible polynomial vector fields on S 2 . We classify all the centers of this class of vector fields and we characterize its global phase portrait.