Hyperbolic growth


Hyperbolic growth

When a quantity grows towards a singularity under a finite variation it is said to undergo hyperbolic growth. This growth is created by non-linear positive feedback mechanisms. Hyperbolic growth is highly nonlinear and it is a stronger form of growth than exponential growth.Fact|date=August 2008

Certain mathematical models suggest that the world population undergoes hyperbolic growth. Of course, the same is true for the exponential growth models that also may be valid for certain time periods only.

Another example of hyperbolic growth can be found in queuing theory: the average waiting time of randomly arriving customers grows hyperbolically as a function of the average load ratio of the server. The singularity in this case occurs when the average amount of work arriving to the server equals the server's processing capacity. If the processing needs exceed the server's capacity, then there is no well-defined average waiting time, as the queue can grow without bound. A practical implication of this particular example is that for highly loaded queuing systems the average waiting time can be extremely sensitive to the processing capacity.

A further practical example of hyperbolic growth can be found in enzyme kinetics. When the the rate of reaction (termed velocity) between an enzyme and substrate is plotted against various concentrations of the substrate, a hyperbolic plot is obtained for many simpler systems. When this happens, the enzyme is said to follow [http://en.wikipedia.org/wiki/Enzyme_kinetics#Michaelis.E2.80.93Menten_kinetics Michaelis-Menton] kinetics.

Mathematical example

References

* [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=1300184&_coverDate=12%2F31%2F2007&_rdoc=6&_fmt=summary&_orig=browse&_srch=doc-info(%23toc%2333783%232007%23999839995%23671853%23FLA%23display%23Volume)&_cdi=33783&_sort=d&_docanchor=&_ct=9&_acct=C000052237&_version=1&_urlVersion=0&_userid=1300184&md5=d9c2663e7fbd6a77385d61334953d75d Alexander V. Markov, and Andrey V. Korotayev (2007). "Phanerozoic marine biodiversity follows a hyperbolic trend". Palaeoworld. Volume 16. Issue 4. Pages 311-318] .
*Kremer, Michael. 1993. "Population Growth and Technological Change: One Million B.C. to 1990," The Quarterly Journal of Economics 108(3): 681-716.

ee also

*Heinz von Foerster
*Technological singularity
*Paradigm shift
*List of paradigm shifts in science
*Scientific mythology
*Social effect of evolutionary theory
*Deep ecology


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