A computation method for non-autonomous systems with discontinuous characteristics. (August 2015)

• Record Type: Journal Article
• Authors: Miino, Yuu; Ito, Daisuke; Ueta, Tetsushi
• Is Part Of: Chaos, solitons and fractals. Volume 77(2015)
• Page Start: 277
• Page End: 285
• Publication Date: 2015-08
• Subjects: Bifurcation phenomena -- Numerical analysis -- Nonlinear non-autonomous system -- Discontinuity; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2015.06.014
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Previous method is not applied to the non-autonomous systems with discontinuity. Regarding the time as the state variable is effective for analyzing such systems. Bifurcation analysis for the forced Izhikevich neuron model has been done. Bifurcation analysis for the forced Alpazur oscillator has been done. Labo experiments for the forced Alpazur oscillator has been done. 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.