Resumo: We will introduce a mathematical model that describes the competition for resources among different ecological species in random environments. Starting from a discrete time model over observation periods, continuous models are developed using diffusion approximation. The resulting system is a system of nonlinear stochastic differential equations, with complex nonlinear structures. Dynamics of the SDE system will be presented to show how environmental fluctuations affect coexistence among species. In particular, we will discuss a two species system under non-stationary environments, and an N species system (N > 2) under stationary environments.
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