Chaotic dynamics in an integro-differential reaction-diffusion system in the presence of 0:1:2 resonance

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2 Citations (Scopus)

Abstract

The dynamics and bifurcation structure of the normal form in the presence of 0:1:2 resonance are studied. It is proved that connecting orbits (heteroclinic cycles or homoclinic orbits) exist on the center manifold of the normal form. Moreover, to study the dynamics around the triple degeneracy of the normal form, we apply the results in Dumortier and Kokubu [4]. The sufficient conditions for the existence of heteroclinic cycles in a scaling family (blow-up vector field) of the 0:1:2 normal form are obtained. These results give a reasonable explanation for the behaviors of the solutions to an integro-reaction-diffusion system.

Original languageEnglish
Title of host publicationMathematical Fluid Dynamics, Present and Future
EditorsYoshihiro Shibata, Yukihito Suzuki
PublisherSpringer New York LLC
Pages531-562
Number of pages32
ISBN (Print)9784431564553
DOIs
Publication statusPublished - 1 Jan 2016
Event8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan
Duration: 11 Nov 201414 Nov 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume183
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014
CountryJapan
CityTokyo
Period11/11/1414/11/14

Keywords

  • 0:1:2 resonance
  • Connecting orbit
  • Heteroclinic loop
  • Normal form

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