Bifurcation of Periodic and Chaotic Solutions in Discontinuous Systems

Michal Feckan

Address. Department of Mathematical Analysis, Comenius University, Mlynska dolina, 842 15 Bratislava, Slovakia


Abstract. Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincare-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given to ordinary differential equations with both dry friction and relay hysteresis terms.

AMS classification. 34A60, 34C25, 58F13, 58F30

Key words. Chaotic and periodic solutions, differential inclusions, relay hysteresis