Border collision route to quasiperiodicity: numerical investigation and experimental confirmation

Zhusubaliyev, Zhanybai T. ; Mosekilde, Erik ; Maity, Somnath ; Mohanan, Srijith ; Banerjee, Soumitro (2006) Border collision route to quasiperiodicity: numerical investigation and experimental confirmation Chaos, 16 (2). 023122_1-023122_11. ISSN 1054-1500

[img]
Preview
PDF - Publisher Version
1MB

Official URL: http://chaos.aip.org/chaoeh/v16/i2/p023122_s1?isAu...

Related URL: http://dx.doi.org/10.1063/1.2208565

Abstract

Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc-dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Bifurcation; Chaos; Numerical Analysis
ID Code:21396
Deposited On:20 Nov 2010 12:58
Last Modified:17 May 2016 05:37

Repository Staff Only: item control page