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A linear birth-and-death predator–prey process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

John Coffey
John Coffey*
Affiliation:
Purdue University Calumet
*
∗ Postal address: Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, IN 46323, USA.
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Abstract

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ1 X and death rate μ1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ2 Y and the death rate is . It is proven that and iff

Keywords

CONTINUOUS-TIME PROBABILISTIC PREDATOR-PREY PROCESSCONDITIONS FOR SURVIVAL

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D50: Animal behavior

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 274 - 277
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research partially supported by LAS Scholarly Research Releases (Fall 1990 and Spring 1991), and by a Purdue Research Foundation Summer Faculty Grant (1991).

References

[1] Alsmeyer, G. (1993) On the Galton-Watson predator-prey process. Ann. Appl. Prob. 3, 198–211.Google Scholar
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[3] Coffey, J. and Bühler, W. J. (1991) The Galton-Watson predator-prey process. J. Appl. Prob. 28, 9–16.Google Scholar
[4] Freedman, D. (1971) Markov Chains. Holden-Day, San Francisco.Google Scholar
[5] Hutton, J. (1980) The recurrence and transience of two-dimensional linear birth and death processes. Adv. Appl. Prob. 12, 615–639.Google Scholar
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