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Stochastic spatial models. (English) Zbl 0940.60086
The author considers a spatial model with the space represented as a grid of sites that can be in one of a finite number of states. The site changes its state with a rate that depends on states of a finite number of sites. Assuming that sites are independent, the behaviour of such models can be studied with the help of mean field ordinary differential equations which describe the evolution of densities of various types [see R. Durrett and S. Levin, Theor. Popul. Biol. 46, No. 3, 363-394 (1994; Zbl 0846.92027)]. The author considers a number of examples (e.g., from population biology) for which the solution of the mean field ODE has one or two attracting points or a periodic orbit.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D40 Ecology
92D25 Population dynamics (general)
92D30 Epidemiology
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