Isocline

Isocline

An Isocline is a series of lines with the same slope. The word comes from the Greek words Isos (Ίδιος) meaning "same" and Klini (κλίση) meaning "slope."

It is often used as a graphical method of solving ordinary differential equations. In an equation of the form "y' = f(x)", the isoclines are given putting "f(x)" 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. 1.

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

References

Hanski, I. (1999) Metapopulation Ecology. Oxford University Press, Oxford, pp. 43-46.

[http://mathworld.wolfram.com/Isocline.html Mathworld: Isocline]


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  • isocline — [ izɔklin ] adj. • 1846; gr. isoklinês, de iso et klinein « pencher » ♦ À inclinaison constante. Géophys. D égale inclinaison magnétique. Lignes isoclines, qui relient sur une carte les points de la Terre où l inclinaison de l aiguille aimantée… …   Encyclopédie Universelle

  • isocline — [ī′sō klīn΄, ī′səklīn΄] n. [see ISOCLINAL] 1. an anticline or syncline so compressed that the strata on both sides of the axis dip with equal inclination in the same direction 2. an isoclinal line …   English World dictionary

  • Isocline — Fig. 1: Isoclines (en bleu), champ de vecteurs (en noir), et quelques courbes solutions (en rouge) de y =xy Les isoclines sont des séries de courbes ayant la même pente. Ce terme provient des mots grecs isos (ισος) pour « même » et… …   Wikipédia en Français

  • isocline — izoklina statusas T sritis Standartizacija ir metrologija apibrėžtis Kreivės ar kreivių šeimos to paties polinkio taškų kreivė. atitikmenys: angl. isoclinal line; isocline vok. Isokline, f rus. изоклина, f pranc. isocline, f …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

  • isocline — izoklina statusas T sritis fizika atitikmenys: angl. isoclinal line; isocline vok. Isokline, f rus. изоклина, f pranc. isocline, f …   Fizikos terminų žodynas

  • Isocline Hill — (coord|83|31|S|157|36|E|) is a hill in the south part of Augen Bluffs, Miller Range. The hill rises 100 200 m above the west side of Marsh Glacier and is connected to Augen Bluffs by a col 10 20 m lower than the height of the hill. So named by… …   Wikipedia

  • isocline — /uy seuh kluyn /, n. Geol. a fold of strata so tightly compressed that both limbs dip in the same direction. [1885 90; back formation from ISOCLINAL] * * * …   Universalium

  • isocline — noun a) A tightly folded syncline or anticline in which the two sides are almost parallel b) Any of a series of lines having the same slope …   Wiktionary

  • isocline — A line in a geographical region that joins all points at which in a population there is the same average frequency for the various alleles at a genetic locus. SEE ALSO: cline. [iso + G. klino, to slope] …   Medical dictionary

  • isocline — (i zo kli n ) adj. Terme scientifique. Qui a la même inclinaison. ÉTYMOLOGIE    Iso..., et du grec, inclinaison …   Dictionnaire de la Langue Française d'Émile Littré

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