Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics

R. Qi, D. Cook, W. Kliemann, V. Vittal

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)


In this paper we consider the visualization of the behavior of high-dimensional dynamical systems by computing the approximated stable manifolds around fixed points using the normal form technique and the energy function method, respectively. By using an effective graphic package called XGobi, we show the high-dimensional invariant manifolds of fixed points of the dynamical system obtained in two different ways, i.e., the normal form method and the energy function method. XGobi allows us to compare different approximations of the invariant manifolds in all dimensions of the system in the same picture, and to analyze the behavior of actual system trajectories in the neighborhood of the fixed point. By viewing in all dimensions, global structural characteristics of the system can be easily detected.

Original languageEnglish
Pages (from-to)175-195
Number of pages21
JournalJournal of Nonlinear Science
Issue number2
Publication statusPublished - 1 Jan 2000
Externally publishedYes


  • Dynamical system
  • Nonlinear
  • Normal form
  • Visualization
  • XGobi

Cite this