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Volume 18   Issue 2   Year 2023
Neverova G.P., Zhdanova O.L.

Complex Dynamics Modes in a Simple Model of Prey-Predator Community: Bistability and Multistability

Mathematical Biology & Bioinformatics. 2023;18(2):308-322.

doi: 10.17537/2023.18.308.

References

  1. Shuntov V.P. Biologiia dal'nevostochnykh morei Rossii (Biology of the Far Eastern seas of Russia). Vladivostok, 2016. 604 p. (in Russ.).
  2. Gorbatenko K.M. Distribution, biomass, and year-to-year dynamics of Sagitta in the Okhotsk Sea. Izvestiya TINRO. 2016;184:168–177 (in Russ.). doi: 10.26428/1606-9919-2016-184-168-177
  3. Dulepova E. Dynamics of zooplankton production parameters in the north-western Bering Sea in the present period. Izvestiya TINRO. 2016;187:187–196 (in Russ.). doi: 10.26428/1606-9919-2016-187-187-196
  4. Dulepova E.P. The current state of plankton communities and food availability for walleye pollock in the western Bering Sea. Trudy VNIRO. 2018;174:91–104 (in Russ.). doi: 10.36038/2307-3497-2018-174-91-104
  5. Dulepova E.P. Sravnitel'naia bioproduktivnost' makroekosistem dal'nevostochnykh morei (Comparative bioproductivity of macroecosystems of the Far Eastern seas). Vladivostok, 2002. 274 p. (in Russ.).
  6. 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
  7. 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
  8. 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
  9. Scheffer M., Rinaldi S., Kuznetsov Y.A., van Nes E.H. Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system. Oikos. 1997:519–532. doi: 10.2307/3546625
  10. Steffen E., Malchow H., Medvinsky A.B. Effects of seasonal perturbations on a model plankton community. Environmental Modeling & Assessment. 1997;2:43–48. doi: 10.1023/A:1019096924487
  11. Medvinskii A.B., Petrovskii S.V., Tikhonova I.A., Tikhonov D.A., Li B.L., Venturino E., Malchow H., Ivanitskii G.R. Spatio-temporal pattern formation, fractals, and chaos in conceptual ecological models as applied to coupled plankton-fish dynamics. Phys. Usp. 2002;45:27–57. doi: 10.1070/PU2002v045n01ABEH000980
  12. Petrovskii S.V., Malchow H. A minimal model of pattern formation in a prey-predator system. Mathematical and Computer Modelling. 1999;29(8):49–63. doi: 10.1016/S0895-7177(99)00070-9
  13. Petrovskii S.V., Malchow H. Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theoretical population biology. 2001;59(2):157–174. doi: 10.1006/tpbi.2000.1509
  14. 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
  15. 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
  16. 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
  17. Bazykin A.D. Matematicheskaia biofizika vzaimodeistvuiushchikh populiatsii (Mathematical biophysics of interacting populations). Moscow, 1985. 182 p. (in Russ.).
  18. 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
  19. 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.
  20. Tyutyunov Yu.V., Titova L.I. From Lotka–Volterra to Arditi–Ginzburg: 90 years of evolving trophic functions. Zhurnal obshchei biologii (Journal of General Biology). 2018;79(6):428–448 (in Russ.). doi: 10.1134/S004445961806009X
  21. 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
  22. 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
  23. Ricker W.E. Metody otsenki i interpretatsii biologicheskikh pokazatelei populiatsii ryb. Moscow, 1979. (Translation of: Ricker W.E. Computation and interpretation of biological statistics of fish populations. Ottawa, 1975).
  24. Frisman Y.Y., 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
  25. 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
  26. Kuznetsov A.P., Sedova Y.V. Bifurcations of three­ and four­dimensional maps: universal properties. Izvestiya VUZ. Applied Nonlinear Dynamics. 2012;20(5):26–43. doi: 10.18500/0869-6632-2012-20-5-26-43
  27. Kuznetsov A.P., Savin A.V., Sedova Iu.V., Tiuriukina L.V. Bifurkatsii otobrazhenii (Images bifurcations). Saratov, 2012. 196 p. (in Russ.).
  28. Kulakov M., Neverova G., Frisman E. The Ricker competition model of two species: dynamic modes and phase multistability. Mathematics. 2022;10(7):1076. doi: 10.3390/math10071076
Table of Contents Original Article
Math. Biol. Bioinf.
2023;18(2):308-322
doi: 10.17537/2023.18.308
published in Russian

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

 

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