The Annals of Applied Probability

Predator-prey and host-parasite spatial stochastic models

Rinaldo B. Schinazi

Full-text: Open access

Abstract

We consider two interacting particle systems on $\mathbf{Z}^d$ to model predator-prey and host-parasite interactions. In both models we have two types of $\mathbf{Z}^d$ particles (1 and 2) and each site in can be in one of four states: empty, occupied by a type 1 particle, occupied by a type 2 particle or occupied by two particles (one of each type). Each type gives birth to particles of the same type on nearest neighbor sites. The interaction between the two types of particles occurs only when a site is occupied by one particle of each type. For both models we show that coexistence and noncoexistence are possible in any dimension.

Article information

Source
Ann. Appl. Probab., Volume 7, Number 1 (1997), 1-9.

Dates
First available in Project Euclid: 14 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1034625250

Digital Object Identifier
doi:10.1214/aoap/1034625250

Mathematical Reviews number (MathSciNet)
MR1428747

Zentralblatt MATH identifier
0880.60099

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Predator-prey host-parasite interacting particle systems

Citation

Schinazi, Rinaldo B. Predator-prey and host-parasite spatial stochastic models. Ann. Appl. Probab. 7 (1997), no. 1, 1--9. doi:10.1214/aoap/1034625250. https://projecteuclid.org/euclid.aoap/1034625250


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