This paper is devoted to the effect of periodic forcing on a system exhibiting a degenerate Hopf bifurcation. Two methods are employed to investigate bifurcations of periodic solution for the periodically forced system. It is obtained by averaging method that the system undergoes fold bifurcation, transcritical bifurcation, and even degenerate Hopf bifurcation of periodic solution. On the other hand, it is also shown by Poincaré map that the system will undergo fold bifurcation, transcritical bifurcation, Neimark-Sacker bifurcation and flip bifurcation. Finally, we make a comparison between these two methods.
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Figure 1.
(a) Phase portrait near a degenerate Hopf bifurcation for
Figure 3.
(b) Bifurcation diagram of the forced system (8) in
Figure 4.
(a) Bifurcation diagram of the forced system (8) in
Figure 5.
(a) Bifurcation diagram of the forced system (26) in
Figure 6.
(a) Bifurcation diagram of the forced system (26) in
Figure 7.
(a) Bifurcation diagram of the forced system (27) in
Figure 9.
(a) Bifurcation diagram of the forced system (28) in
Figure 10.
Phase portraits and Poincaré section of the periodically forced system. (a) A stable period-two orbit in system (27) for
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