stationary point,
n.
1a. also called (North American usage) critical point. a point on a curve at which its first derivative is zero, so that the tangent is parallel to the axis of the independent variable (that is, in the usual two-dimensional Cartesian coordinate system, it is horizontal, as at P in the figure below); a maximum, minimum or point of inflection.
b. more generally, a point at which the gradient or similar variation of a function vanishes.
P is a stationary point. 2. a set of values of the state variables of a system of autonomous differential equations y' = f(y) that make the system f(y0) zero; these are characterized by having constant solution y(t) = y0. Since dy/dt = 0, these points are also singular, all other points being regular.
1a. also called (North American usage) critical point. a point on a curve at which its first derivative is zero, so that the tangent is parallel to the axis of the independent variable (that is, in the usual two-dimensional Cartesian coordinate system, it is horizontal, as at P in the figure below); a maximum, minimum or point of inflection.
b. more generally, a point at which the gradient or similar variation of a function vanishes.