Geometrical concepts and computational techniques of nonlinear dynamics

Geometrical concepts and computational techniques of nonlinear dynamics

This paper presents a brief overview of some of the geometrical concepts of nonlinear dissipative dynamics. Computational techniques are described for locating fixed points of Poincaré maps, local bifurcations and homoclinic tangencies of invariant manifolds and following them as parameters vary. Th...

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Veröffentlicht in:Computer methods in applied mechanics and engineering 1991-08, Vol.89 (1), p.381-394
Hauptverfasser: Foale, S., Thompson, J.M.T.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
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Zusammenfassung:This paper presents a brief overview of some of the geometrical concepts of nonlinear dissipative dynamics. Computational techniques are described for locating fixed points of Poincaré maps, local bifurcations and homoclinic tangencies of invariant manifolds and following them as parameters vary. The cell to cell mapping technique for locating basins of attraction in a computationally efficient way is outlined.
ISSN:0045-7825
1879-2138
DOI:10.1016/0045-7825(91)90049-C