Controlling Hopf bifurcations of discrete-time systems in resonance
作者： Daolin Xu , Jianhua Xie , Guilin Wen
DOI: 10.1016/J.CHAOS.2004.07.002
关键词: Bogdanov–Takens bifurcation 、 Transcritical bifurcation 、 Hopf bifurcation 、 Control theory 、 Biological applications of bifurcation theory 、 Mathematical analysis 、 Saddle-node bifurcation 、 Bifurcation theory 、 Mathematics 、 Bifurcation diagram 、 Pitchfork bifurcation
摘要: Abstract Resonance in Hopf bifurcation causes complicated behaviors. To design with certain desired characteristics the resonance cases of discrete-time systems, a feedback control method is developed. The controller designed aid washout filters. law constructed according to criticality and stability conditions bifurcations as well constraints. gains associated linear terms insure creation nonlinear determine type bifurcated solutions. derive former, we propose implicit criteria eigenvalue assignment transversality condition for creating parameter location. latter, technique center manifold reduction, Iooss’s theory Wan’s are employed. In numerical experiments, show circles fixed points from created strong weak four-dimensional system.
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