Intermittent operation of linear driven switched systems

The phenomenon of breathing (intermittent operation) is studied in a class of piecewise continuous systems as well as its relation with system parameters. The class of systems under study comprises a continuous time subsystem and a switching rule that induces an oscillatory path by switching alternately between stable and unstable conditions. An interesting feature of the system is that eigenvalues of linear subsystems play an important role in system evolution. It is shown that although regular and chaotic phases evolve irregularly for a given system, their average behavior is surprisingly regular with respect to a bifurcation parameter. It is found that the phenomenon of breathing share some structural characteristics with intermittency; i.e. existence of a critical exponent. However, for switched systems, many critical exponents may be required. Bifurcation maps and other analysis tools allow us to gain insight into the origin of breathing. This work constitutes a first step toward the characterization of intermittent operation in piecewise continuous systems.