Hopf bifurcations in nonautonomous systems at points of resonance.

Details Hopf bifurcations in nonautonomous systems at points of resonance. Hopf bifurcations in nonautonomous systems at points of resonance.

Feb 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990sccha..33..206c&link_type=abstract

Science in China, Series A, Vol. 33, No. 2, p. 206 - 219

Physics

1

Celestial Mechanics: Resonances

Scientific paper

Hopf bifurcation in periodically time-dependent systems are studied at points of resonance. By a new normal form, it is proved that the Poincaré map has an invariant cycle emerging from the origin for some degenerate bifurcations. While for nondegenerate bifurcations, of primary interest is the case of 1:4 resonance, the existence and uniqueness of invariant cycle are proved when there is no nonzero fixed point.

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