Multimodal oscillations in systems with strong contraction
type: Item
instance of: scholarly article
title: Multimodal oscillations in systems with strong contraction
zbMATH Open document ID: 1126.34025
author: N. E. Zubov
published in: Physica D
publication date: 2007-05-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0701417
review text: The authors consider a 3-dimension system of ordinary differential equations, which is obtained by a finite dimensional approximation for the interface dynamics in a free boundary problem modeling solid fuel combustion. By varying two system parameters, Hopf bifurcation boundaries with both super- and subcritical postbifurcation behaviour are found. In the supercritical regime a series of periodic doubling bifurcations is observed, where the double frequency is primarly generated by the center manifold reduction for the stable mode. In the subcritical case a Shilnikov-like scenario is found with multimodal solutions and arbitrarily long intervals between successive large amplitude oscillations. Also a chaotic attractor followed by a reverse period-doubling cascade is numerically observed in this parameter region. The existence of these solutions is analytically established by constructing an appropriate return map close to the unstable stationary point.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C60
zbMATH DE Number: 5156583
zbMATH Keywords: Andronov Hopf bifurcation
zbMATH Keywords: solid fuel combustion
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: supercritical bifurcation
zbMATH Keywords: subcritical bifurcation
zbMATH Keywords: multimodal orbits
reviewed by: Alois Steindl
MaRDI profile type: Publication
OpenAlex ID: W2169165140
arXiv ID: math/0701417
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DOI: 10.1016/J.PHYSD.2007.02.011
description: scientific article