CHAOS IN A SPATIAL EPIDEMIC MODEL
成果类型：
Article
署名作者：
Durrett, Rick; Remenik, Daniel
署名单位：
Cornell University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/08-AAP581
发表日期：
2009
页码：
1656-1680
关键词：
摘要：
We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the d-dimensional lattice and torus, with d >= 2. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjecture that on the infinite lattice with a fixed finite dispersal distance, distant parts of the lattice oscillate out of phase so there is a unique nontrivial stationary distribution.
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