Chaos in a Stochastic Spatial Model
Rick Durrett and Daniel Remenik
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 the two-dimensional lattice, torus, and
random 3-regular graph. 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 non-trivial stationary distribution.
Preprint Annals of Applied Probability, to appear
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