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 Poincaré 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.
@article{miino2015computation,
author = {Miino, Yuu and Ito, Daisuke and Ueta, Tetsushi},
title = {{A computation method for non-autonomous systems with discontinuous characteristics}},
journal = {Chaos, Solitons and Fractals},
publisher = {Elsevier},
year = {2015},
month = {6},
volume = {77},
pages = {277--285},
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 Poincaré 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.},
doi = {10.1016/j.chaos.2015.06.014},
scope = {international},
review = {reviewed},
langid = {english}
}