Periodic forcing on degenerate Hopf bifurcation. (English) Zbl 1472.34074
In this work, the authors deal with 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 the 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. The method is novel and enriches the bifurcation theory of delayed differential equation to some degree.
Reviewer: Changjin Xu (Guiyang)
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 34C29 | Averaging method for ordinary differential equations |
| 37C60 | Nonautonomous smooth dynamical systems |
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