Abstract:
The paper studies dynamic modes of the Ricker model with the periodic Malthusian parameter. The equation parametric space is shown to have multistability areas in which different dynamic modes are possible depending on the initial conditions. In particular, the model trajectory can asymptotically tend either to a stable cycle or to a chaotic attractor. Oscillation synchronization of the 2-cycles and the Malthusian parameter of the model are studied. Fluctuations in population size and environmental factors can be either synchronous or asynchronous. The structural features of attraction basins in phase space are investigated for possible stable dynamic modes.
Citation:
K. V. Shlufman, G. P. Neverova, E. Ya. Frisman, “Dynamic modes of the Ricker model with periodic Malthusian parameter”, Nelin. Dinam., 13:3 (2017), 363–380
\Bibitem{ShlNevFri17}
\by K.~V.~Shlufman, G.~P.~Neverova, E.~Ya.~Frisman
\paper Dynamic modes of the Ricker model with periodic Malthusian parameter
\jour Nelin. Dinam.
\yr 2017
\vol 13
\issue 3
\pages 363--380
\mathnet{http://mi.mathnet.ru/nd571}
\crossref{https://doi.org/10.20537/nd1703005}
\elib{https://elibrary.ru/item.asp?id=29993266}
Linking options:
https://www.mathnet.ru/eng/nd571
https://www.mathnet.ru/eng/nd/v13/i3/p363
This publication is cited in the following 7 articles:
E. Ya. Frisman, M. P. Kulakov, “Ot lokalnoi bi- i kvadrostabilnosti k prostranstvenno-vremennoi neodnorodnosti: obzor matematicheskikh modelei i soderzhatelnye sledstviya”, Kompyuternye issledovaniya i modelirovanie, 15:1 (2023), 75–109
E. Ya. Frisman, O. L. Zhdanova, M. P. Kulakov, G. P. Neverova, O. L. Revutskaya, “Mathematical modeling of population dynamics based on recurrent equations: results and prospects. Part I”, Biol. Bull, 48:1 (2021), 1–15
G. P. Neverova, O. L. Zhdanova, E. A. Kolbina, A. I. Abakumov, “Planktonnoe soobschestvo: vliyanie zooplanktona na dinamiku fitoplanktona”, Kompyuternye issledovaniya i modelirovanie, 11:4 (2019), 751–768
E. Ya. Frisman, K. V. Shlufman, G. P. Neverova, “Dynamics of satellite population related species with cyclical dynamics”, Biol. Bull, 46:4 (2019), 317–326
M. Yu. Khavinson, A. N. Kolobov, “Modelirovanie dinamiki chislennosti zanyatogo naseleniya v otraslyakh ekonomiki: agent-orientirovannyi podkhod”, Kompyuternye issledovaniya i modelirovanie, 10:6 (2018), 919–937
K. V. Shlyufman, G. P. Neverova, E. Ya. Frisman, “Fazovaya multistabilnost kolebatelnykh rezhimov dinamiki modeli Rikera s periodicheski izmenyayuschimsya maltuzianskim parametrom”, Matem. biologiya i bioinform., 13:1 (2018), 68–83
E.Ya. Frisman, K.V. Shlufman, G.P. Neverova, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 7, Proceedings of the International Conference “Mathematical Biology and Bioinformatics”, 2018