非线性系统的定性相图构造

提出了一种新的基于定性仿真的非线性动力系统相图构造方法。首先对在定性仿真中应用最为广泛的QSIM算法进行改进,提出了适合于非线性系统的基于具体代数约束表示的仿真算法。在此基础上,对二维分叉系统以及非奇异的三维系统的相图构造实践进行实例分析。结果表明这种方法是完全可行的,它能够捕捉到所有定性可区分的系统行为从而很好的弥补传统的基于数值积分的相图构造方法的缺陷,因而具有其不可替代的价值。

Computing Qualitative Phase Portraits of Nonlinear System

This paper provides a new qualitative simulation based method to construct phase portrait of nonlinear system. First, it provides an enhanced qualitative simulation algorithm based on special algebraic constraint representation, which is fit for nonlinear systems. Then it attempts to construct phase portrait of a planar bifurcation system and a non-strange three-dimensional system. The results demonstrate that this method is totally feasible. It can capture all qualitatively distinct system behavior, which overcomes the limits of traditional phase construction approach based on numeric integration very well, and thereby has ins own value.