从Hopf分岔到极限环

试图通过几何的直观性考察定性与分支理论在Hopf分岔产生极限环中的应用.利用计算机模拟具体的Hopf分岔过程,并且以一种更自然的方式给出Hopf分岔的Liapunov方法定理和证明.在此基础上对多个极限环的产生和奇点变性问题做了初步探讨.介绍了研究分支问题的思想方法和应用实例,并对其方法进行了比较评述.

From Hopf bifurcation to limit cycle

Emphasizes the geometrical understanding of the application of qualitative and bifurcation theories in the process of Hopf bifurcation leading to limit circle.Illustrating an example of Hopf bifurcation by using the computer,we showed the proof of Liapunov method theorem in a much more comprehensible way.Based on previous work,we made a primary study on the generating of more limit cycles and on the change of singular point.Then we made an introduction of the methods to study the bifurcation and an interesting application,and made short comments on these two kinds of method at the end.