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Time-dependent solution of the logistic model for population growth in random environment

Published online by Cambridge University Press:  14 July 2016

Prajneshu
Prajneshu*
Affiliation:
Birkbeck College, London
*
∗Postal address: Department of Statistics, Birkbeck College, London WC 1E 7HX, U.K.
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Abstract

The exact time-dependent solution as well as the stationary solution of the logistic model for population growth with varying carrying capacity is worked out in both the Stratonovich and Ito calculi by solving the forward Kolmogorov equation.

Keywords

FORWARD KOLMOGOROV EQUATIONLOGISTIC MODELSTRATONOVICH AND ITO CALCULITIME-DEPENDENT SOLUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 4 , December 1980 , pp. 1083 - 1086
Copyright
Copyright © Applied Probability Trust 

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References

Erdelyi, A. (1953) Higher Transcendental Functions, Vols. 1 and 2. McGraw-Hill, New York.Google Scholar
Feldman, M. W. and Roughgarden, J. (1975) A population's stationary distribution and chance of extinction in a stochastic evironment with remarks on the theory of species packing, Theoret. Popn Biol. 7, 197–207.Google Scholar
Wong, E. (1964) The construction of a class of stationary Markoff processes. Proc. Symp. Appl. Math. XVI, 264–276.Google Scholar