CONTINUOUS APPROXIMATION OF DYNAMICAL-SYSTEMS WITH RANDOMLY MATCHED INDIVIDUALS

Biologists and economists have analyzed populations in which each individual interacts with randomly selected individuals. Because random matching generates a very complicated stochastic process, biologists and economists frequently approximate the population dynamics by a deterministic process. This paper examines the limit of random matching schemes as the population grows, matches occur very frequently, and the proportion of the population paired in a matching becomes very small. In the limit, the population evolves according to a differential equation. The proof of convergence depends either on the existence of a global attractor or on finiteness of the time horizon. (C) 1995 Academic Press, Inc.