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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
EN
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.
2
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A nonlocal coagulation-fragmentation model

75%
Lachowicz M., Wrzosek D.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 1
45-66
EN
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.
3
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A kinetic equation for repulsive coalescing random jumps in continuum

63%
Pilorz K.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2016
|
tom 70
|
nr 1
EN
A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of solutions of the corresponding kinetic equation are proved.
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