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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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