A simple stochastic model for a complex ecosystem

We investigate the role of the noise on the transient dynamics of a simple ecosystem composed of many interacting species. We assume that the species interact randomly. The influence of the environment is modelled by a multiplicative noise. We study the dynamics of the ecosystem for two values of the growth parameter. We obtain the transient and the asymptotic behaviour of the average population of the species and the distributions of the population and of the local field. Numerical results are compared with analytical asymptotic behaviours of the time average of the with species.