一种三阶自治电路系统动力学行为的分岔算法及仿真

A Bifurcation Algorithm and Simulation of Kinetic Behavior of a 3rd-order Autonomous Circuit System

自治电路系统有两种最为常见的分岔模式,即静态分岔和Hopf分岔。在一定的条件下,系统的平衡点可以通过这两种分岔模式改变其运动状态。基于分岔理论,分析了平衡点分岔的条件,给出了相应的分岔集,得出了相关算法;通过数值计算验证了分岔集的存在性;并应用Multisim软件设计搭建了实验电路。

There are two most common bifurcation modes for the autonomous circuit system,namely static bifurcation and Hopf bifurcation.Under certain conditions,the system balance point can change its motion state through these two bifurcated modes. Based on the bifurcation theory,this paper analyzes the conditions for the bifurcation of the balance point,presents corresponding bifurcation sets,and obtains related algorithms. Existence of the bifurcation set is verified through numerical calculation. An experimental circuit is designed and set up by using Multisim software.