J. Wiser and M. Golubitsky
Bifurcations in Forced Response Curves
SIAM J. Appl. Dynam. Sys.
Submitted.
The "forced response curve" is a graph showing the amplitude of the response
of a periodically forced system as the forcing frequency is varied. Zhang
and Golubitsky (SIADS, 10(4) (2011) 1272-1306) classified the existence and
multiplicity of periodic responses to small amplitude periodic forcing of a
system near a Hopf bifurcation point, where the forcing frequency, omega_F,
is close to the Hopf frequency, omega_H. They showed that there are six kinds
of forced response curves when viewed as bifurcation diagrams with omega = omega_H - omega_F
as the distinguished bifurcation parameter. In this paper we show that there
are 41 possible bifurcation diagrams when stability, as well as multiplicity,
of the periodic solutions in the forced response curves is included.