Limit cycles of continuous and discontinuous piecewise-linear differential systems in R3

Abstract

We study the limit cycles of two families of piecewise-linear differential systems in R 3 with two pieces separated by a plane Σ . In one family the differential systems are continuous on the plane Σ , and in the other family they are discontinuous on the plane Σ . The usual tool for studying these limit cycles is the Poincaré map, but here we shall use recent results which extend the averaging theory to continuous and discontinuous differential systems. All the computations have been done with the algebraic manipulator Mathematica.