Characterization of the role of fluctuations in predator-prey dynamics driven by demographic stochasticity

Abstract

The objectives of this paper is to model, simulate and analyse stochastic fluctuations of predator-prey dynamics by resorting to van Kampen system-size expansion and Gillespie algorithm. The master equation has been formulated and use the perturbation method proposed by van Kampen which provides the Fokker-Planck equation describing the time evolution of the unknown probability distribution governing the statistics of the fluctuations. The Gillespie algorithm was used to simulate the master equations that denotes the transition of the state of the system according to a Markov process. These two approaches in stochastic analysis proved to provide a more detailed description of the system.