An Stochastic Model for Population Dynamics in Multi-patch Systems

Abstract

Abstract In this thesis we developed a mathematical model using stochastic differential equa- tions in order to model three interacting populations. We first presented some his- torical remarks about populations in patchy environments. We also discussed briefly the dynamical behavior, random varying and stochastic effects (birth, death, migra- tion) on animal populations. We also introduced basic concepts of metapopulations. We also discussed concepts from probability theory, Itˆ formula, system of stochastic o differential equation and Brownian motion-Wiener process. We presented briefly the numerical solutions of SDE’s using Euler-Maruyama method. We described a general stochastic modelling approach for multi-patch systems, and hence we droved a formula for three interacting populations.