Russian version English version
Volume 17   Issue 2   Year 2022
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 & Bioinformatics. 2022;17(2):465-480.

doi: 10.17537/2022.17.465.

References

  1. Carlotti F., Giske J., Werner F. Modeling zooplankton dynamics. In: ICES zooplankton methodology manual. Academic Press, 2000. P. 571–667. doi: 10.1016/B978-012327645-2/50013-X
  2. Leles S.G., Valentin J.E.L., Figueiredo G.M. Evaluation of the complexity and performance of marine planktonic trophic models. Anais da Academia Brasileira de Ciências. 2016;88:1971–1991. doi: 10.1590/0001-3765201620150588
  3. Berdnikov S.V., Selyutin V.V., Surkov F.A., Tyutyunov Yu.V. Modeling of marine ecosystems: experience, modern approaches, directions of development (Review). Part 2. Population and trophodynamic models. Physical Oceanography. 2022;29(2):182–203. doi: 10.22449/1573–160X-2022-2–182-203
  4. Scheffer M., Rinaldi S., Kuznetsov Y.A. Effects of fish on plankton dynamics: a theoretical analysis. Canadian Journal of Fisheries and Aquatic Sciences. 2000;57(6):1208–1219. doi: 10.1139/f00-018
  5. Medvinsky A.B., Tikhonova I.A., Aliev R.R., Li B.L., Lin Z.S., Malchow H. Patchy environment as a factor of complex plankton dynamics. Physical Review E. 2001;64(2):021915. doi: 10.1103/PhysRevE.64.021915
  6. Chattopadhayay J., Sarkar R. R., Mandal S. Toxin-producing plankton may act as a biological control for planktonic blooms – field study and mathematical modelling. Journal of Theoretical Biology. 2002;215(3):333–344. doi: 10.1006/jtbi.2001.2510
  7. Zhang Z., Rehim M. Global qualitative analysis of a phytoplankton–zooplankton model in the presence of toxicity. International Journal of Dynamics and Control. 2017;5(3):799–810. doi: 10.1007/s40435-016-0230-5
  8. Svirezhev Yu.M., Logofet D.O. Stability of Biological Communities. MIR Publishers, 1983.
  9. Svirezhev Yu.M. Nonlinearities in mathematical ecology: Phenomena and models. Would we live in Volterra’s world? Ecological Modelling. 2008;216:89–101. doi: 10.1016/j.ecolmodel.2008.03.028
  10. Tyutyunov Yu.V., Titova L.I., Surkov F.A., Bakaeva E.N. Trophic function of phytophagous rotifers (rotatoria). Experiment and modeling. Biology Bulletin Reviews. 2010;71(1):52–62.
  11. Adamson M. W., Morozov A. Y. When can we trust our model predictions? Unearthing structural sensitivity in biological systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2013;469(2149):20120500. doi: 10.1098/rspa.2012.0500
  12. Tyutyunov Yu.V., Titova L.I. Zhurnal obshchei biologii (Journal of General Biology). 2018;79(6):428–448.(in Russ.).
  13. Giricheva E. The Influence of Trophic Interactions in the Plankton Community on Its Spatiotemporal Dynamics. Mathematical Biology and Bioinformatics. 2019;14(2):393–405. doi: 10.17537/2019.14.393
  14. Medvinsky A.B., Rusakov A.V., Tikhonov D.A., Nurieva N.I., Tereshko V.M., Adamovich B.V. Population Dynamics: Mathematical Modeling and Reality. Biophysics. 2019;64(6):956-977. doi: 10.1134/S0006350919060150
  15. Bazykin A.D. Matematicheskaia biofizika vzaimodeistvuiushchikh populiatsii (Mathematical biophysics of interacting populations). Moscow, 1985. 182 p. (in Russ.).
  16. Abrams P.A., Ginzburg L.R. The nature of predation: prey dependent, ratio dependent or neither? Trends in Ecology & Evolution. 2000;15(8):337–341. doi: 10.1016/S0169-5347(00)01908-X
  17.  Abakumov A.I., Pak S.Y., Morozov M.A., Tynybekov A.K. Model Estimation of the Phytoplankton Biomass of Lake Issyk-Kul Using Remote Sensing Data. Inland Water Biology. 2019;12(Suppl. 2):111–118. doi: 10.1134/S0320965219060020
  18. Shambarova Yu.V., Stepochkin I.E., Zakharkov S.P. Verification of VGPM and K&I models of primary production in the northwestern part of the Japan Sea using shipboard and satellite data. Current Problems in Remote Sensing of the Earth from Space. 2019;16(2):186–195. doi: 10.21046/2070-7401-2019-16-2-186-195
  19. Abakumov A.I., Izrailsky Yu.G. Models of phytoplankton distribution over chlorophyll in various habitat conditions. Estimation of aquatic ecosystem bioproductivity. Computer Research and Modeling. 2021;13(6):1177–1190. doi: 10.20537/2076-7633-2021-13-6-1177-1190
  20. Frisman E.Ya., Kulakov M.P., Revutskaya O.L., Zhdanova O.L., Neverova G.P. The key approaches and review of current researches on dynamics of structured and interacting populations. Computer Research and Modeling. 2019;11(1):119–151. doi: 10.20537/2076-7633-2019-11-1-119-151
  21. Neverova G.P., Zhdanova O.L., Abakumov A.I. Discrete-Time Model of Seasonal Plankton Bloom. Mathematical Biology and Bioinformatics. 2020;15(2):235–250. doi: 10.17537/2020.15.235
  22. Frisman E.Y., Zhdanova O.L., Kulakov M.P., Neverova G.P., Revutskaya O.L. Mathematical modeling of population dynamics based on recurrent equations: results and prospects. Part I. Biology Bulletin. 2021;48(1):1–15. doi: 10.1134/S1062359021010064
  23. Arditi R., Ginzburg L.R. Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 1989;139(3):311–326. doi: 10.1016/S0022-5193(89)80211-5
  24. Fan Y.H., Li W.T. Permanence for a delayed discrete ratio-dependent predator–prey system with Holling type functional response. Journal of Mathematical Analysis and Applications. 2004;299(2):357–374. doi: 10.1016/j.jmaa.2004.02.061
  25. Liu R., Gao J. Permanence for a delayed discrete ratio-dependent N-species predator–prey system with Holling-type II functional response. Mathematical and Computer Modelling. 2010. doi: 10.1016/j.mcm.2010.11.085
  26. Berezovskaya F., Karev G., Arditi R. Parametric analysis of the ratio-dependent predator–prey model. Journal of Mathematical Biology. 2001;43(3):221–246. doi: 10.1007/s002850000078
  27. Morozov A., Arashkevich E., Reigstad M., Falk-Petersen S. Influence of spatial heterogeneity on the type of zooplankton functional response: a study based on field observations. Deep Sea Research Part II: Topical Studies in Oceanography. 2008;55(20–21):2285–2291. doi: 10.1016/j.dsr2.2008.05.008
  28. Irigoien X., Flynn K.J., Harris R.P. Phytoplankton blooms: a ‘loophole’in microzooplankton grazing impact? Journal of Plankton Research. 2005;27(4):313–321. doi: 10.1093/plankt/fbi011
  29. Morozov A., Abbott K.C., Cuddington K., Francis T., Gellner G., Hastings A., Lai Y.C., Petrovskii S.V., Scranton K., Zeeman M.L. Long transients in ecology: Theory and applications. Physics of Life Reviews. 2020;32:1–40. doi: 10.1016/j.plrev.2019.09.004

 

Table of Contents Original Article
Math. Biol. Bioinf.
2022;17(2):465-480
doi: 10.17537/2022.17.465
published in Russian

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

 

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