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{{for|a type of geological structure|Isocline (geology)}}
[[image:Isocline 3.png|thumb|right|300px|Fig.&thinsp;1: Isoclines (blue), slope field (black), and some solution curves (red) of ''y''' =&thinsp;''xy''. The solution curves are <math>y = C e^{x^2/2}</math>.]]
Given a [[family of curves]], assumed to be [[Differentiable manifold|differentiable]], an '''isocline''' for that family is formed by the [[set (mathematics)|set]] of points at which some member of the family attains a given [[slope]]. The word comes from the [[Greek language|Greek]] words [[:wikt:ἴσος|ἴσος]] (isos), meaning "same", and the [[:wikt:κλίνειν|κλίνειν]] (klenein), meaning "make to slope". Generally, an isocline will itself have the shape of a curve or the [[union (set theory)|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''(''x'',&thinsp;''y''), the isoclines are lines in the (''x'',&thinsp;''y'') plane obtained by setting ''f''(''x'',&thinsp;''y'') equal to a constant.  This gives a series of lines (for different constants) 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.&thinsp;1.

==Other uses==
In [[population dynamics]], the term "zero-growth 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.<ref>{{cite web |title=INTERSPECIFIC COMPETITION: LOTKA-VOLTERRA |url=http://www.tiem.utk.edu/~gross/bioed/bealsmodules/competition.html |accessdate=6 March 2019 |archive-url=https://web.archive.org/web/20210517195628/http://www.tiem.utk.edu/~gross/bioed/bealsmodules/competition.html |archive-date=17 May 2021 |url-status=dead}}</ref> However, this is rare and a more common term is [[nullcline]].

==References==
{{Reflist}}
*Hanski, I.  (1999) Metapopulation Ecology.  Oxford University Press, Oxford, pp.&nbsp;43–46.
*[http://mathworld.wolfram.com/Isocline.html Mathworld: Isocline]

[[Category:Ordinary differential equations]]