Chaos in a spatial epidemic model

Rick Durrett, Daniel Remenik
2009 The Annals of Applied Probability  
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 $d\geq2$. 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
more » ... r 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.
doi:10.1214/08-aap581 fatcat:cc4osdbcwfbphosfvgewood6am