Markov chain model of phytoplankton dynamics

Radosław Wieczorek

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 4, page 763-771
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Radosław Wieczorek. "Markov chain model of phytoplankton dynamics." International Journal of Applied Mathematics and Computer Science 20.4 (2010): 763-771. <http://eudml.org/doc/208024>.

@article{RadosławWieczorek2010,
abstract = {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.},
author = {Radosław Wieczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {phytoplankton dynamics; coagulation; fragmentation; Markov chain},
language = {eng},
number = {4},
pages = {763-771},
title = {Markov chain model of phytoplankton dynamics},
url = {http://eudml.org/doc/208024},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Radosław Wieczorek
TI - Markov chain model of phytoplankton dynamics
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 4
SP - 763
EP - 771
AB - 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.
LA - eng
KW - phytoplankton dynamics; coagulation; fragmentation; Markov chain
UR - http://eudml.org/doc/208024
ER -

References

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  2. Aldous, D. (1999). Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists, Bernoulli 5(1): 3-48. Zbl0930.60096
  3. Arino, O. and Rudnicki, R. (2004). Phytoplankton dynamics, Comptes Rendus Biologies 327(11): 961-969. 
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  6. Ethier, S.N. and Kurtz, T.G. (1986). Markov Processes: Characterization and Convergence, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, NY. Zbl0592.60049
  7. Franks, P.J.S. (2002). NPZ models of plankton dynamics: Their construction, coupling to physics, and application, Journal of Oceanography 58(2): 379-387. 
  8. Henderson, P.A. (2003). Practical Methods in Ecology, WileyBlackwell, Malden, MA. 
  9. Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons Ltd, Chichester. Zbl1197.62135
  10. Jackson, G. (1990). A model of the formation of marine algal flocs by physical coagulation processes, Deep-Sea Research 37(8): 1197-1211. 
  11. Laurençot, P. and Mischler, S. (2002). The continuous coagulation-fragmentation equations with diffusion, Archive for Rational Mechanics and Analysis 162(1): 45-99. Zbl0997.45005
  12. Levin, S.A. and Segel, L.A. (1976). Hypothesis for origin of planktonic patchiness, Nature 259. 
  13. Passow, U. and Alldredge, A. (1995). Aggregation of a diatom bloom in a mesocosm: The role of transparent exopolymer particles (TEP), Deep-Sea Research II 42(1): 99-109. 
  14. Rudnicki, R. and Wieczorek, R. (2006a). Fragmentationcoagulation models of phytoplankton, Bulletin of the Polish Academy of Sciences: Mathematics 54(2): 175-191. Zbl1105.60076
  15. Rudnicki, R. and Wieczorek, R. (2006b). Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1(1): 83-100. Zbl1201.92062
  16. Rudnicki, R. and Wieczorek, R. (2008). Mathematical models of phytoplankton dynamics, Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (1): 55-63. 
  17. Wieczorek, R. (2007). Fragmentation, coagulation and diffusion processes as limits of individual-based aggregation models, Ph.D. thesis, Institute of Mathematics, Polish Academy of Sciences, Warsaw, (in Polish). 
  18. Young, W., Roberts, A. and Stuhne, G. (2001). Reproductive pair correlations and the clustering of organisms, Nature 412(6844): 328-331. 

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