Equilibrium position
of a system of ordinary differential equations
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A point such that
is a solution of
(constant in time). The solution itself is also called an equilibrium position. A point is an equilibrium position of
if and only if
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Let be an arbitrary solution of . The change of variables
transforms this solution into the equilibrium position
of the system
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Therefore, in stability theory, for example, it is possible to assume, without loss of generality, that the problem always consists of investigating the stability of an equilibrium position at the origin in .
The equilibrium position of a non-autonomous system
is often called the trivial solution, zero solution, singular point, stationary point, rest point, equilibrium state, or fixed point.
Equilibrium position. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Equilibrium_position&oldid=18108