Double hopf bifurcation with strong resonances in delayed systems with nonlinerities

J. Xu; K. W. Chung

doi:10.1155/2009/759363

Author(s)

J. Xu
K. W. Chung

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Article number	759363
Journal / Publication	Mathematical Problems in Engineering
Volume	2009
Publication status	Published - 2009

Link(s)

DOI	DOI https://doi.org/10.1155/2009/759363 Final Published version
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Attachment(s)	Documents 5678438.pdf Final Published version, 2.17 MB, PDF Publisher's Copyright Statement This full text is made available under CC-BY 3.0. https://creativecommons.org/licenses/by/3.0/
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-75649131176&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(7ae9f53c-7cb3-47c6-9587-0631aa437cf2).html

Abstract

An efficient method is proposed to study delay-induced strong resonant double Hopf bifurcation for nonlinear systems with time delay. As an illustration, the proposed method is employed to investigate the 1:2 double Hopf bifurcation in the van der Pol system with time delay. Dynamics arising from the bifurcation are classified qualitatively and expressed approximately in a closed form for either square or cubic nonlinearity. The results show that 1:2 resonance can lead to codimension-three and codimension-two bifurcations. The validity of analytical predictions is shown by their consistency with numerical simulations.