TY - GEN
T1 - Parametrically excited Hopf bifurcation with non-semisimple 1:1 resonance
AU - Namachchivaya Sri, N.
AU - Malhotra, Naresh
PY - 1992
Y1 - 1992
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:0026962760
SN - 0791810925
T3 - American Society of Mechanical Engineers, Design Engineering Division (Publication) DE
SP - 29
EP - 46
BT - Nonlinear Vibrations
PB - Publ by ASME
T2 - Winter Annual Meeting of the American Society of Mechanical Engineers
Y2 - 8 November 1992 through 13 November 1992
ER -