Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
Nonlinear Systems
verfasst von : J. David Logan
Erschienen in: A First Course in Differential Equations
Verlag: Springer New York
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
If a nonlinear system has an equilibrium, then the behavior of the orbits near that point is often mirrored by a linear system obtained by discarding the small nonlinear terms. We already know from Chapter 6 how to analyze linear systems; their behavior is determined by the eigenvalues of the associated matrix for the system. Therefore the general idea is to approximate the nonlinear system by a linear system in a neighborhood of the equilibrium and use the properties of the linear system to deduce the properties of the nonlinear system. This analysis, which is standard fare in differential equations, is called
local stability analysis
.