Russian version English version
Volume 18   Issue 2   Year 2023
Abakumov A.I., Kozitskaya I.S.

Mathematical Model of Phytoplankton Interspecific Competition for Food Resource

Mathematical Biology & Bioinformatics. 2023;18(2):568-579.

doi: 10.17537/2023.18.568.


  1. Moiseev P.A. Biologicheskie resursy Mirovogo okeana (Biological resources of the World Ocean). Moscow, 1989 (in Russ.).
  2. Menshutkin, V.V., Rukhovets L.A., Filatov N.N. Ecosystem modeling of freshwater lakes (review): 2. Models of freshwater lake's ecosystem. Water Resources. 2014;41(1):32–45. doi: 10.1134/S0097807814010084
  3. Falkowski P.G. The Ocean invisible fores. Scientific American. 2002;54:54–61. doi: 10.1038/scientificamerican0802-54
  4. Finenko Z.Z., Suslin V.V., Churilova T.Ya. The Regional Model to Calculate the Black Sea Primary Production Using Satellite Color Scanner Seawifs. Marine Biological Journal. 2009;8(1):81–106 (in Russ.).
  5. Pak S.Ya., Abakumov A.I. Phytoplankton in the Sea of Okhotsk along Western Kamchatka: warm vs cold years. Ecological Modelling. 2020;433(1). Article No. 109244. doi: 10.1016/j.ecolmodel.2020.109244
  6. Edwards A.M., Brindley J. Oscillatory behaviour in a three-component plankton population model. Dynamics and Stability of Systems. 1996;11(4ggg):347–370. doi: 10.1080/02681119608806231
  7. Ilyash L.V., Radchenko I.G., Kuznetsov L.L., Lisitzyn A.P., Novigatskiy A.N., Martynova D.M., Chul'tsova A.L. Spatial Variability of The Species Composition, Abundance, and Productivity of the Phytoplankton in the White Sea in the Late Summer Period. Oceanology. 2011;51(1):19-26. doi: 10.1134/S000143701101005X
  8. Zakharkov S.P., Lobanov V.B., Gordeichuk T.N., Shtraikhert E.A., Morozova T.V. Spatial variability of the chlorophyll a and the specific structure of the phytoplankton in the northwestern part of the sea of japan during the winter period. Oceanology. 2012;52(3):354-363. doi: 10.1134/S0001437012020105
  9. Jang S.J., Baglama J. Nutrient-plankton models with nutrient recycling. Computers & Mathematics with Applications. 2005;49(2–3):375–387. doi: 10.1016/j.camwa.2004.03.013
  10. Geider R., MacIntyre H., Kana T. A dynamic regulatory model of phytoplanktonic acclimation to light, nutrients, and temperature. Limnology and Oceanography. 1998;43(4):679–694. doi: 10.4319/lo.1998.43.4.0679
  11. Neverova G.P., Zhdanova O.L. Comparative Dynamics Analysis of Simple Mathematical Models of the Plankton Communities Considering Various Types of Response Function. Mathematical Biology and Bioinformatics. 2022;17(2):465–480. doi: 10.17537/2022.17.465
  12. Platt T., Sathyendranath S. Estimators of primary production for interpretation of remotely sensed data on ocean color. Journal of Geophysical Research. 1993;98(C8):14561–14576. doi: 10.1029/93JC01001
  13. Kuznetsova A.V., Pogosyan S.I.. Voronova E.N., Konyukhov I.V., Rubin A.B. Nitrogen deficit impact on growth and condition of photosynthetic apparatus of green algae Chlamydomonas reinhardtii. Voda: khimiia i ekologiia (Water: chemistry and ecology). 2012(4):68–76 (in Russ.).
  14. Mairet F., Bernard O., Lacour T., Sciandra A. Modelling microalgae growth in nitrogen limited photobioreactor for estimating biomass, carbohydrate and neutral lipid productivities. IFAC Proceedings. 2011;44:10591–10596. doi: 10.3182/20110828-6-IT-1002.03165
  15. Silkin V.A., Abakumov A.I., Pautova L.A., Pakhomova S.V., Lifanchuk A.V. Mechanisms of regulation of invasive processes in phytoplankton on the example of the north-eastern part of the Black Sea. Aquatic Ecology. 2016;50(2):221–234. doi: 10.1007/s10452-016-9570-7
  16. Abakumov A.I., Pak S.Ya. Modeling of Photosynthesis Process and Assessing of Phytoplankton Dynamics Based on Droop Model. Mathematical Biology and Bioinformatics. 2021;16(2):380–393. doi: 10.17537/2021.16.380
  17. Abakumov A.I., Pak S.Ya. Two Approaches to Modeling Phytoplankton Biomass Dynamics Based on the Droop Model. Mathematical Biology and Bioinformatics. 2022;17(2):401–422. doi: 10.17537/2022.17.401
  18. DeAngelis D.L. Dynamics of nutrient cycling and food webs. Springer, 2012. 288 p. doi: 10.1007/978-94-011-2342-6
  19. Elsgolts L. Differential Equations and the Calculus of Variations. University Press of the Pacific, 2003. P. 444.
  20. Vasiliev V.A., Romanovsky Yu.M., Yakhno V.G. Autowave Processes. Moscow: Nauka; 1987. 240 p. (in Russ.). doi: 10.1007/978-94-009-3751-2_8
  21. Kuznetsov S.P. Dinamicheskii khaos (Dynamic Chaos). Moscow; 2001. 296 p. (in Russ.).
  22. Turing A.M. The Chemical Basis of Morphogenesis. In: Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences. 1952;237(641):37–72. doi: 10.1098/rstb.1952.0012
  23. Longhurst A., Sathyendranath S., Platt T., Caverhill C. An estimate of global primary production in the ocean from satellite radiometer data. Journal of Plankton Research. 1995;17(6):1245–1271. doi: 10.1093/plankt/17.6.1245
  24. Romanovsky Yu.M., Stepanova N.V., Chernavsky D.S. Mathematical Biophysics. Moscow: Nauka; 1984. 304 p. (in Russ.).
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2023.18.568
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)


  Copyright IMPB RAS © 2005-2024