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Markov chain model of phytoplankton dynamics

100%

Wieczorek R.

International Journal of Applied Mathematics and Computer Science

2010

tom 20

nr 4

763-771

A discrete-time stochastic spatial model of plankton dynamics is given. We focus on aggregative behaviour of plankton cells. Our aim is to show the convergence of a microscopic, stochastic model to a macroscopic one, given by an evolution equation. Some numerical simulations are also presented.

A nonlocal coagulation-fragmentation model

75%

Lachowicz M., Wrzosek D.

Applicationes Mathematicae

2000

tom 27

nr 1

45-66

A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.

Ograniczanie wyników

1 Applicationes Mathematicae

1 International Journal of Applied Mathematics and Computer Science

1 Lachowicz M.

1 Wieczorek R.

1 Wrzosek D.

1 2010

1 2000

Wyniki wyszukiwania

Markov chain model of phytoplankton dynamics

A nonlocal coagulation-fragmentation model