带弹簧的瓦特调速器中的Hopf分岔
Hopf Bifurcations in a Watt Governor With a Spring
摘要：
本文继续了作者在“六角调速系统的稳定性和Hopf分支”中的研究，重点研究了六角Watt调速系统的余维一Hopf分支。研究了余维2、3、4的Hopf分支，确定了相应的Lyapunov稳定性系数和分支图，给出了分支小振幅周期轨道的数目、类型和位置。结果发现，在参数空间中存在一个开放区域，在该区域中，两个吸引周期轨道与一个吸引平衡点共存。
英文摘要：
This paper pursues the study carried out by the authors in "Stability and Hopf bifurcation in a hexagonal governor system", focusing on the codimension one Hopf bifurcations in the hexagonal Watt governor differential system. Here are studied the codimension two, three and four Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, ilustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found an open region in the parameter space where two attracting periodic orbits coexist with an attracting equilibrium point.
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