Mathematical Biology & Bioinformatics | 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

Shuntov V.P. Biologiia dal'nevostochnykh morei Rossii (Biology of the Far Eastern seas of Russia). Vladivostok, 2016. 604 p. (in Russ.).
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
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
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
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.).
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
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
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
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
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
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
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
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
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
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
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
Bazykin A.D. Matematicheskaia biofizika vzaimodeistvuiushchikh populiatsii (Mathematical biophysics of interacting populations). Moscow, 1985. 182 p. (in Russ.).
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
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.
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
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
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
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).
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
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
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
Kuznetsov A.P., Savin A.V., Sedova Iu.V., Tiuriukina L.V. Bifurkatsii otobrazhenii (Images bifurcations). Saratov, 2012. 196 p. (in Russ.).
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