Geometric integration of stochastic Lotka-Volterra equations

In this thesis, Stratonovich noise terms are introduced into the Lotka-Volterra equations while still maintaining the Poisson property of the flow. Three stochastic Poisson models are proposed. The first stochastic model adds stochasticity to the interaction of the species, the second stochastic model adds stochasticity to the death and birth rates of the populations and the last proposed stochas- tic model adds stochasticity to the frequency of the periodic solutions. Additionally a stochastic Poisson integrator is proposed and its performance is tested against a non-geometric integrator.