Local Bifurcations of Nonlinear Hybrid Systems

Abstract—As most analysis tools for nonlinear dynam-ical systems are dedicated to either continuous or discrete models, we propose an analysis method for hybrid systems. Using the Poincare ́ map, we transform the results of par-tial analysis over the continuous components into a discrete mapping. We can then apply more conventional methods in order to seek for critical values and obtain bifurcation dia-grams in the parameters space. In this paper, we describe this method, discuss different approaches to conduct such analysis, and finally present an application example with a 3-state Alpazur oscillator. 1