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On Lotka–Volterra predator prey models

Published online by Cambridge University Press:  14 July 2016

L. Billard
L. Billard*
Affiliation:
Florida State University
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Abstract

Ever since Lotka (1925) and Volterra (1926), (1931) first considered mathematical formulations for prey-predator processes, the resultant equations have resisted attempts to solve them. However, over the intervening 50 years, standard techniques have allowed a few isolated results to be obtained for some simplified versions of the original process, but the classical equations for the stochastic model have remained unsolved. We give here solutions to the classical process for the case in which interactions occur over a sufficiently short period of time that no births occur. The technique used is one recently developed by Severo (1969a), (1969b), (1971). The approach can be easily generalised to allow solution for the case in which births do occur, as well as for the simplified versions of the original process.

Keywords

LOTKA–VOLTERRA PREY-PREDATOR MODELSSTATE PROBABILITIESSTOCHASTIC MODEL
Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 375 - 381
Copyright
Copyright © Applied Probability Trust 1977 

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