Computational methods in nonlinear stability analysis: stability boundary calculations

A numerical method is presented for the estimation and the visualization of the stability boundary of an equilibrium point in the state space of autonomous nonlinear dynamical systems. The technique uses a combination of certain concepts from Liapunov theory, numerical simulation and the properties...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2004-07, Vol.168 (1-2), p.289-297
Main Authors: Luyckx, L., Loccufier, M., Noldus, E.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Liapunov theory
Mathematics
Sciences and techniques of general use
Split boundary value problems
Stability boundary calculations
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Visualization
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Summary:A numerical method is presented for the estimation and the visualization of the stability boundary of an equilibrium point in the state space of autonomous nonlinear dynamical systems. The technique uses a combination of certain concepts from Liapunov theory, numerical simulation and the properties of the geometric structure of the stability boundary. The boundary can be visualized by computing its intersections with arbitrarily selected two-dimensional planes in state space. The visualization problem is reduced to a two-point boundary value differential problem which is solved using a flooding technique.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2003.05.021