LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS
International Journal of Bifurcation and Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 21, n. 11, p. 3181-3194, 2011.
Universidade Estadual Paulista (Unesp)
Univ Autonoma Barcelona
We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in R(n) perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed.