Phase plane

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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.


  • [a1] O. Hajek, "Dynamical systems in the plane", Acad. Press (1968)
How to Cite This Entry:
Phase plane. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.V. Anosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article