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BORDER COLLISION BIFURCATIONS IN THREE-DIMENSIONAL PIECEWISE SMOOTH SYSTEMS

INDRAVA ROY

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

Institut fur Mathematik, University of Paderborn, 33098 Paderborn, Germany

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and

A. R. ROY

Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India

Author for correspondence.

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https://doi.org/10.1142/S0218127408020495Cited by:11 (Source: Crossref)

Abstract

Piecewise smooth maps have been a focus of study for scientists in a wide range of research fields. These maps show qualitatively different types of bifurcations than those exhibited by generic smooth maps. We present a theoretical framework for analyzing three-dimensional piecewise smooth maps by deriving a suitable normal form and then finding the stability criteria for periodic orbits. We also show by numerical simulation different types of border collision bifurcations that can occur in such a map. We have also been able to observe a border collision bifurcation from a period-2 to a quasiperiodic orbit.

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