Parametrically excited Hopf bifurcation with non-semisimple 1:1 resonance

N Sri Namachchivaya, Naresh Malhotra

Research output: Chapter in Book/Report/Conference proceedingConference contribution


A generalized four dimensional, nonlinear and non-autonomous system is studied. The effect of periodic parametric excitations is examined on systems that exhibit Hopf bifurcation with one to one resonance along with subharmonic external resonance. The linear operator is assumed to have a generic nonsemisimple structure. In this case, the dimensionality of the system can not be reduced despite the presence of an S1 symmetry. However, the system is simplified considerably by reducing it to the corresponding four dimensional normal form equations. The local behavior of the equilibrium solutions is studied along with their stability properties. Several codimension 1, 2 and 3 bifurcation varieties are observed. Some of the global bifurcations that are present, can be associated with the Bogdanov Takens and {0, +i, -i} bifurcation varieties. The numerical results, obtained by using AUTO and CHAOS, indicate the existence of homoclinic orbits along with the period doubling behavior which leads to chaos.

Original languageEnglish (US)
Title of host publicationNonlinear Vibrations
PublisherPubl by ASME
Number of pages18
ISBN (Print)0791810925
StatePublished - 1992
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA
Duration: Nov 8 1992Nov 13 1992

Publication series

NameAmerican Society of Mechanical Engineers, Design Engineering Division (Publication) DE


OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAnaheim, CA, USA

ASJC Scopus subject areas

  • Engineering(all)


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