Proceeding of International Conference
Quentin Brandon, Tetsushi Ueta, Takuji Kousaka, Daniele Fournier-Prunaret, Local Bifurcations of Nonlinear Hybrid Systems, Proc. NOLTA'07, 160-163, Vancouver, Sep. 2007.
Abstract: As most analysis tools for nonlinear dynamical systems are dedicated to either continuous or discrete models, we propose an analysismethod for hybrid systems. Using the Poincar´e map, we transform the results of partial analysis over the continuous components into a discrete mapping. We can then apply more conventionalmethods in order to seek for critical values and obtain bifurcation diagrams 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.