周期激励Stuart-Landau方程的某些动力学行为

Some Dynamical Behavior of the Stuart-Landau Equation With a Periodic Excitation

研究了周期激励Stuart＿Landau方程的锁频周期解· 利用奇异性理论分别研究了这些解关于外部激励振幅和频率的分岔行为· 结果表明:关于外部激励振幅的普适开折具有余维3,在某些条件下,得到了转迁集及分岔图· 另外还证明:关于频率的分岔问题具有无穷余维,因此该情形下的动力学分岔行为非常复杂· 发现了一些新的动力学现象。

The lock-in periodic solutions of the Stuart-Landau equation with a periodic excitation are studied. Using singularity theory, the bifurcation behavior of these solutions with respect to the excitation amplitude and frequency are investigated in detail, respectively.The results show that the universal unfolding with respect to the excitation amplitude possesses codimension 3. The transition sets in unfolding parameter plane and the bifurcation diagrams are plotted under some conditions. Additionally, it has also been proved that the bifurcation problem with respect to frequence possesses infinite codimension. Therefore the dynamical bifurcation behavior is very complex in this case. Some new dynamical phenomena are presented, which are the supplement of the results obtained by Sun Liang et al.