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・ Hyperbole
・ Hyperbole and a Half
・ Hyperbolic
・ Hyperbolic 3-manifold
・ Hyperbolic absolute risk aversion
・ Hyperbolic angle
・ Hyperbolic coordinates
・ Hyperbolic Dehn surgery
・ Hyperbolic discounting
・ Hyperbolic distribution
・ Hyperbolic equilibrium point
・ Hyperbolic function
・ Hyperbolic geometric graph
・ Hyperbolic geometry
・ Hyperbolic group
Hyperbolic growth
・ Hyperbolic law of cosines
・ Hyperbolic link
・ Hyperbolic manifold
・ Hyperbolic motion
・ Hyperbolic motion (relativity)
・ Hyperbolic navigation
・ Hyperbolic orthogonality
・ Hyperbolic partial differential equation
・ Hyperbolic plane (disambiguation)
・ Hyperbolic point
・ Hyperbolic quaternion
・ Hyperbolic secant distribution
・ Hyperbolic sector
・ Hyperbolic set


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Hyperbolic growth : ウィキペディア英語版
Hyperbolic growth

When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth.〔See, e.g., Korotayev A., Malkov A., Khaltourina D. (Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth ). Moscow: URSS Publishers, 2006. P. 19-20.〕 More precisely, the reciprocal function 1/x has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as x \to 0 is infinite: any similar graph is said to exhibit hyperbolic growth.
==Description==
If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value x_0, the function will exhibit hyperbolic growth, with a singularity at x_0.
In the real world hyperbolic growth is created by certain non-linear positive feedback mechanisms.〔See, e.g., Alexander V. Markov, and Andrey V. Korotayev (2007). ("Phanerozoic marine biodiversity follows a hyperbolic trend". Palaeoworld. Volume 16. Issue 4. Pages 311-318 ).〕

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