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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 $dgeq2$. 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.
We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process supercritical.
We prove a shape theorem for the set of infected individuals in a spatial epidemic model with 3 states (susceptible-infected-recovered) on ${mathbb Z}^d,dge 3$, when there is no extinction of the infection. For this, we derive percolation estimates (
We investigate the behavior in $N$ of the $N$--particle entropy functional for Kacs stochastic model of Boltzmann dynamics, and its relation to the entropy function for solutions of Kacs one dimensional nonlinear model Boltzmann equation. We prove a
Motivated by models of cancer formation in which cells need to acquire $k$ mutations to become cancerous, we consider a spatial population model in which the population is represented by the $d$-dimensional torus of side length $L$. Initially, no sit
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets interspersed with sho