Math @ Duke

Publications [#243539] of Richard T. Durrett
Papers Published
 Durrett, R; Remenik, D, Chaos in a spatial epidemic model,
The Annals of Applied Probability, vol. 19 no. 4
(August, 2009),
pp. 16561685, Institute of Mathematical Statistics, ISSN 10505164 [MR2010k:60322], [doi]
(last updated on 2019/06/24)
Abstract: 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 3regular graph and on the ddimensional 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. © Institute of Mathematical Statistics, 2009.


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