Geodesic
Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System
Y. Sekerci1 ; S. Petrovskii1
1 Department of Mathematics, University of Leicester,University Road, Leicester LE1 7RH, U.K.
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 96-114.

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Oxygen production due to phytoplankton photosynthesis is a crucial phenomenon underlying the dynamics of marine ecosystems. However, most of the existing literature focus on other aspects of the plankton community functioning, thus leaving the issue of the coupled oxygen-plankton dynamics understudied. In this paper, we consider a generic model of the oxygen-phytoplankton-zooplankton dynamics to make an insight into the basic properties of the plankton-oxygen interactions. The model is analyzed both analytically and numerically. We first consider the nonspatial model and show that it predicts possible oxygen depletion under certain environmental conditions. We then consider the spatially explicit model and show that it exhibits a rich variety of spatiotemporal patterns including travelling fronts of oxygen depletion, dynamical stabilization of unstable equilibrium and spatiotemporal chaos.
DOI : 10.1051/mmnp/201510207

Y. Sekerci 1 ; S. Petrovskii 1

1 Department of Mathematics, University of Leicester,University Road, Leicester LE1 7RH, U.K. 
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Y. Sekerci; S. Petrovskii. Mathematical Modelling of Spatiotemporal Dynamics of Oxygen in a Plankton System. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 96-114. doi : 10.1051/mmnp/201510207. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201510207/

[1] M. Abbott. Phytoplankton patchiness: ecological implications and observation methods. In: Patch dynamics (Levin, S.A., Powell, T.M., Steele, J.H., eds.), Lecture Notes in Biomathematics vol. 96. Springer, Berlin, 1993, pp. 37–49.

[2] W. Allegretto, C. Mocenni, A. Vicino J. Math. Biol. 2005 367 388

[3] M. Banerjee, S.V. Petrovskii Theoretical Ecology 2011 37 53

[4] M. Bengfort, U. Feudel, F.M. Hilker, H. Malchow Ecological Complexity 2014 185 194

[5] J. Chattopadhyay, S. Pal Ecological Modelling 2002 15 28

[6] L. Edelstein-Keshet. Mathematical models in biology. Random House, New York, 1988.

[7] A.M. Edwards, J. Brindley Bull. Math. Biol. 1999 303 339

[8] M.J.R. Fasham Oceanogr. Mar. Biol. Annu. Rev. 1978 43 79

[9] T. Gaarder, H.H. Gran Cons. Int. Explor. Mer. 1927 3 48

[10] M. Guysinsky, B. Hasselblatt, V. Rayskin Discr. Contin. Dyn. Syst. 2003 979 984

[11] G.P. Harris. Phytoplankton ecology. Structure function and fluctuation. Chapman and Hall, USA, 1986.

[12] V. Hulla, L. Parrell, M. Falcucci Ecol. Model. 2008 468 480

[13] K. Rutledge Geophys. Res. Lett. 2004 L22301

[14] Y.A. Kuznetsov. Elements of applied bifurcation theory. Applied Mathematical Sciences vol. 112. Springer, Berlin, 1995.

[15] T.K. Leen Phys. Lett. 1993 89 93

[16] N.D. Lewis, A. Morozov, M.N. Breckels, M. Steinke, E.A. Codling Math. Model. Nat. Phenom. 2015 25 44

[17] F. Mackas, C.M. Boyd Science 1979 62 64

[18] H. Malchow Proc. R. Soc. Lond. B. 1993 103 109

[19] H. Malchow, S.V. Petrovskii Mathematical and Computer Modelling 2002 307 319

[20] H. Malchow, S.V. Petrovskii, F. Hilker Nova Acta Leopoldina 2003 325 340

[21] H. Malchow, S.V. Petrovskii, E. Venturino. Spatiotemporal patterns in ecology and epidemiology: theory, models, simulations. Mathematical and Computational Biology Series. Chapman and Hall / CRC Press, Boca Raton, 2008.

[22] N. Marchettini, C. Mocenni, A. Vicino Annali di Chimica 1999 505 514

[23] A.K. Misra Nonlinear Analysis: Modeling and Control 2010 185 198

[24] C. Mocenni. Mathematical modelling of coastal systems: engineering approaches for parameter identification, validation and analysis of the models. Unpublished manuscript, (2006), available at http://web.univ-ubs.fr/lmam/frenod/SiteGdmEtGdm2/GGDDMM/03D22BA4-6225-46CC-8968-D8621FBFD967˙files/confMocenni.pdf.

[25] A.S. Monin, A.M. Yaglom. Statistical fluid mechanics, Vol. 1. MIT Press, Cambridge MA, 1971.

[26] B. Moss. Ecology of Freshwaters, 4th edition. John Willey, Chichester, 2010.

[27] A. Okubo. Diffusion and ecological problems: mathematical models. Springer-Verlag, Berlin, 1980.

[28] E. Paasche. Pelagic production in nearshore waters. In: Nitrogen cycling in coastal marine environments (Blackburn H., Sorensen J., eds.), John Wiley, Chichester, 1988, 33–58.

[29] M. Pascual Proc. R. Soc. Lond. B. 1993 1 7

[30] S.V. Petrovskii, H. Malchow Nonlinear Analysis: Real World Applications 2000 37 51

[31] S.V. Petrovskii, H. Malchow. Mathematical models of marine ecosystems. In: The Encyclopedia of Life Support Systems (EOLSS). Developed under the Auspices of the UNESCO. Eolss Publishers, Oxford, 2005. [http://www.eolss.net]

[32] S.V. Petrovskii, K. Kawasaki, F. Takasu, N. Shigesada Japan Journal of Industrial and Applied Mathematics 2001 459 481

[33] S. Rinaldi, R. Soncini-sessa, H. Stehfest, H. Tamura. Modeling and control of river quality. McGraw-Hill, 1979.

[34] L.A. Segel, J.L. Jackson J. Theor. Biol. 1972 545 559

[35] J.A. Sherratt, M.A. Lewis, A.C. Fowler Proc. Natl. Acad. Sci. USA 1995 2524 2528

[36] I.R. Smith Freshwater Biol. 1982 445 449

[37] J.H. Steele. Spatial pattern in plankton communities, Plenum Press, New York, 1978.

[38] J.H. Steele, E.W. Henderson Am. Nat. 1981 676 691

[39] A.A. Voinov, A.P. Tonkikh Ecol. Model. 1987 211 226

[40] V. Volpert, S. Petrovskii Phys. Life Rev. 2009 267 310

[41] M. Warkentin, H.M. Freese, U. Karsten, R. Schumann Applied and Environmental Microbiology 2007 6722 6729

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