A computation method for non-autonomous systems with discontinuous characteristics

作者：Miino Yuu^*; Ito Daisuke; Ueta Tetsushi

来源：Chaos Solitons & Fractals, 2015, 77: 277-285.

DOI：10.1016/j.chaos.2015.06.014

• Bifurcation phenomena
• Numerical analysis
• Nonlinear non-autonomous system
• Discontinuity

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.

• 出版日期2015-8