Yuu Miino, Daisuke Ito, Tetsushi Ueta, A computation method for non-autonomous systems with discontinuous characteristics, Elsevier, Chaos, Solitons & Fractals, Vol.77, No.8, 277-285, June 2015.
Abstract: We propose a computation method to obtain bifurcation sets of periodic solutions in non-autonomous systems with discontinuous properties. If the system has discontinuity for the states and/or the vector field, conventional methods cannot be applied. We have developed a method for autonomous systems with discontinuity by taking the Poincare mapping on the switching point in the preceded study, however, this idea does not work well for some non-autonomous systems with discontinuity. We overcome this difficulty by extending the system to an autonomous system. As a result, bifurcation sets of periodic solutions are solved accurately with a shooting method. We show two numerical examples and demonstrate the corresponding laboratory experiment.