Growth function exhibiting a singularity at a finite time
When a quantity grows towards a singularity under a finite variation (a "finite-time singularity") it is said to undergo hyperbolic growth.[1] More precisely, the reciprocal function has a hyperbola as a graph, and has a singularity at 0, meaning that the limit as is infinite: any similar graph is said to exhibit 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.
finite variation (a "finite-time singularity") it is said to undergo hyperbolicgrowth. More precisely, the reciprocal function 1 / x {\displaystyle 1/x}...
characteristic of hyperbolic geometry Hyperbolicgrowth, growth of a quantity toward a finite-time singularity Hyperbolic logarithm, original designation of...
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...
in finite time, it is called hyperbolicgrowth. In between exponential and hyperbolicgrowth lie more classes of growth behavior, like the hyperoperations...
Exponential growth, also called geometric growthHyperbolicgrowth Linear growth, refers to two distinct but related notions Logistic growth, characterized...
build out as synergy and the completion as maturity. Cross fluid Hyperbolicgrowth Heaviside step function Hill equation (biochemistry) Hubbert curve...
the apparent hyperbolicgrowth of the human population in the past, instead of a simpler exponential growth. It is proposed that the growth rate is accelerating...
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...
precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely generated group...
hyperbola (/haɪˈpɜːrbələ/ ; pl. hyperbolas or hyperbolae /-liː/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in a plane, defined...
shown that till the 1970s the hyperbolicgrowth of the world population was accompanied by quadratic-hyperbolicgrowth of the world GDP, and developed...
limitation, or both. The hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the human population growth arises from quadratic...
Hyperbole (/haɪˈpɜːrbəli/ ; adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is the use of exaggeration as a rhetorical device or figure of speech. In rhetoric, it is...
modern science. Fat-tailed distribution Heavy-tailed distributions Hyperbolicgrowth Lévy flight Long tail Pareto distribution Power-law fluid Simon model...
In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...
population size and the rate of technological growth. The hyperbolic character of biodiversity growth can be similarly accounted for by a feedback between...
information growth, such as Moore's law or computer intelligence, is projected into the future, resulting in exponential growth or hyperbolicgrowth (to a singularity)...
shown that till the 1970s the hyperbolicgrowth of the world population was accompanied by quadratic-hyperbolicgrowth of the world GDP, and developed...
Models (2008). Of special interest is his research in the World System hyperbolicgrowth. Apart from the quantitative study of electoral and party systems...
project in crocheting a patch of the hyperbolic plane, and provides an initial warning about the exponential growth in the area of this plane as a function...
In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number...
to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial...
an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric space. This...
developed a number of mathematical models of the World System population hyperbolicgrowth and the global demographic transition. His activities in science popularization...