Particle Systems and Reaction-Diffusion Equations: connecting micro and macro models
Steve Krone, Mathematics, University of Idaho (April 16, 2012)
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This will be something of an introductory talk that considers two types of spatial models used in population biology, and connections between them. Interacting particle systems can be thought of as "microscopic" level descriptions of populations, including interactions between discrete individuals and stochasticity. Reaction-diffusion equations provide deterministic models that can be thought of as "macroscopic" versions of particle systems through scaling limits. We will discuss the basic ideas behind this connection, treat a few examples, and try to understand the extent to which the two types of models predict the same behavior.