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	~~In [[population dynamics]]~~, ~~'''Nurgaliev's law'''~~ is an equation that describes the rate of change of the size of a population at a given time, in terms of the current population size. It is a deterministic [[ordinary differential equation]] in which the rate of change is expressed as a [[quadratic function]] of the population size.		Nice to satisfy you, my title is Araceli Oquendo but I don't like when individuals use my complete title. Bookkeeping is what I do for a residing. The factor she adores most is to perform handball but she can't make it her occupation. Delaware has usually been my living place and will never move.<br><br>Also visit my web page ... [http://Mcdonnell.Exiondev.com/node/325 extended car warranty]

	~~==Specification==~~

	~~Nurgaliev's law is expressed as~~

	~~:<math>{dn \over dt} = an^2 - bn,</math>~~

	~~where 'n' is the size of a population, '~~'t'' is ~~time measured in years, ''a'' is a half of the average probability of a birth of a male (the same~~ for ~~females) of~~ a ~~potential arbitrary parents pair within a year, ''b'' is an average probability of a death of a person within a year~~.

	The ~~first term~~ is ~~twice proportional~~ to ~~the half of population (number of males and number of females)~~. ~~The second term is responsible for [[death rate]] and~~ has ~~a clear~~ and precise sense— death rates are constant in time but vary with position on the age scale (babies are at risk at birth, the middle aged are at risk of [[Physical trauma\|trauma]], old men become ill). It is known to [[demography\|demographers]], for example, that the probability of death within the first year of a life is precisely equal to similar probability for the 55th year of a life.{{Citation needed\|date=September 2011}} Thus, in the given model, the average person dies under the same law as an unstable [[atomic nucleus]] decays.{{Citation needed\|date=September 2011}}

	~~==Stability==~~

	~~The population has steady states at~~ <~~math~~> ~~n = 0, b/a~~ <~~/math~~>. The state with <math> n=0 </math> is stable whereas the state with <math> n=b/a </math> is unstable, meaning that the equation describes a population which crashes (tends to zero) when the death rate is greater than the birth rate and explodes (tends to infinity) when it is the birth rate that is greater.

	~~{{No footnotes\|date=September 2011}}~~
	~~==Sources==~~
	*"'Law' of Two Hundred Billions in Context of Civil Society". In materials of Inter-regional scientific-practical conference ''The Civil Society: Ideas, Reality, Prospects'', Kazan-Zelenodolsk; on April 27, 2006, p. 204-207. ISBN 5-8399-0153-9.
	*Nurgaliev I.S., "Kinematics of Demography", Report on 9th Global Strategic Forum. http://~~gsf~~.~~inesnet~~.ru/~~?p=161~~

	~~[[Category:Demography]]~~
	~~[[Category:Population models]~~]


	~~{{sociology-stub}}~~

en>David Eppstein: WP:NOTED

2013-03-31T20:18:14Z

WP:NOTED

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+In [[population dynamics]], '''Nurgaliev's law''' is an equation that describes the rate of change of the size of a population at a given time, in terms of the current population size. It is a deterministic [[ordinary differential equation]] in which the rate of change is expressed as a [[quadratic function]] of the population size.
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+Nurgaliev's law is expressed as

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