Isocline


Given a family of curves, assumed to be differentiable, an isocline for that family is formed by the set of points at which some member of the family attains a given slope. The word comes from the Greek words :wikt:ἴσος|ἴσος, meaning "same", and the :wikt:κλίνειν|κλίνειν, meaning "make to slope". Generally, an isocline will itself have the shape of a curve or the union of a small number of curves.
Isoclines are often used as a graphical method of solving ordinary differential equations. In an equation of the form y' = f, the isoclines are lines in the plane obtained by setting f equal to a constant. This gives a series of lines along which the solution curves have the same gradient. By calculating this gradient for each isocline, the slope field can be visualised; making it relatively easy to sketch approximate solution curves; as in fig. 1.

Other uses

In population dynamics, the term "isocline" refers to the set of population sizes at which the rate of change for one population in a pair of interacting populations is zero.