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A stochastic model of symbiosis

Urszula Skwara — 2010

Annales Polonici Mathematici

We consider a system of stochastic differential equations which models the dynamics of two populations living in symbiosis. We prove the existence, uniqueness and positivity of solutions. We analyse the long-time behaviour of both trajectories and distributions of solutions. We give a biological interpretation of the model.

A stochastic symbiosis model with degenerate diffusion process

Urszula Skwara — 2010

Annales Polonici Mathematici

We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.

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