Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 175-195 |
| Number of pages | 21 |
| Journal | Journal of Nonlinear Science |
| Volume | 10 |
| Issue number | 2 |
| State | Published - Mar 2000 |
| Externally published | Yes |
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Keywords
- Dynamical system
- Nonlinear
- Normal form
- Visualization
- XGobi
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mathematics(all)
- Applied Mathematics
- Mathematical Physics
- Statistical and Nonlinear Physics
Cite this
Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics. / Qi, R.; Cook, D.; Kliemann, W.; Vittal, Vijay.
In: Journal of Nonlinear Science, Vol. 10, No. 2, 03.2000, p. 175-195.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Visualization of stable manifolds and multidimensional surfaces in the analysis of power system dynamics
AU - Qi, R.
AU - Cook, D.
AU - Kliemann, W.
AU - Vittal, Vijay
PY - 2000/3
Y1 - 2000/3
N2 - 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.
AB - 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.
KW - Dynamical system
KW - Nonlinear
KW - Normal form
KW - Visualization
KW - XGobi
UR - http://www.scopus.com/inward/record.url?scp=0012728532&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0012728532&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0012728532
VL - 10
SP - 175
EP - 195
JO - Journal of Nonlinear Science
JF - Journal of Nonlinear Science
SN - 0938-8974
IS - 2
ER -