Sensitivity to Model Structure in a Stochastic Rosenzweig-MacArthur Model Driven by a Compound Poisson Process

Abstract

In this thesis we study the matter of hypersensitivity to model structure in the Rosenzweig- MacArthur predator-prey model, and in particular whether the introduction of stochasticity reduces the sensitivity of the !-limit sets to small changes in the underlying vector field. To do this, we study the steady-state probability distributions of stochastic differential equations driven by a compound Poisson process on a bounded subset of Rn, as steady-state distributions are analogous to !-limit sets for stochastic differential equations. We take a primarily analytic approach, showing that the steady-state distributions are equivalent to weak measure-valued solutions to a certain partial differential equation. We then analyze perturbations of the underlying vector field using tools from the theory of compact operators. Finally, we numerically simulate and compare solutions to both the deterministic and stochastic versions of the Rosenzweig-MacArthur model.