Difference between revisions of "Phase plane"
From Encyclopedia of Mathematics
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| − | The plane $\mathbf R^2$, which can be used for a geometrical interpretation of an [[ | + | The plane $\mathbf R^2$, which can be used for a geometrical interpretation of an [[autonomous system]] of two first-order ordinary differential equations (or one second-order ordinary differential equation). A phase plane is a special case of a [[phase space]]. |
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| + | See also [[Dynamical system]] (where this interpretation is called kinematic); [[Qualitative theory of differential equations]]; [[Poincaré–Bendixson theory]]. | ||
====References==== | ====References==== | ||
| − | + | * {{Ref|a1}} O. Hajek, "Dynamical systems in the plane", Acad. Press (1968) | |
Latest revision as of 14:12, 8 April 2023
The plane $\mathbf R^2$, which can be used for a geometrical interpretation of an autonomous system of two first-order ordinary differential equations (or one second-order ordinary differential equation). A phase plane is a special case of a phase space.
See also Dynamical system (where this interpretation is called kinematic); Qualitative theory of differential equations; Poincaré–Bendixson theory.
References
- [a1] O. Hajek, "Dynamical systems in the plane", Acad. Press (1968)
How to Cite This Entry:
Phase plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Phase_plane&oldid=32014
Phase plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Phase_plane&oldid=32014
This article was adapted from an original article by D.V. Anosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article