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Nelin. Dinam., 2016, Volume 12, Number 4, Pages 553–565 (Mi nd537)  

This article is cited in 4 scientific papers (total in 4 papers)

Original papers

Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability

K. V. Shlufmana, G. P. Neverovab, E. Ya. Frismana

a Institute for Complex Analysis of Regional Problems, Far Eastern Branch of RAS, ul. Sholom-Aleikhem 4, Birobidzhan, 679016, Russia
b Institute of Automation and Control Processes, Far Eastern Branch of RAS, ul. Radio 5, Vladivostok, 690041, Russia

Abstract: This paper investigates the emergence and stability of 2-cycles for the Ricker model with the 2-year periodic Malthusian parameter. It is shown that the stability loss of the trivial solution occurs through the transcritical bifurcation resulting in a stable 2-cycle. The subsequent tangent bifurcation leads to the appearance of two new 2-cycles: stable and unstable ones. As a result, there is multistability. It is shown that the coexistence of two different stable 2-cycles is possible in a narrow area of the parameter space. Further stability loss of the 2-cycles occurs according to the Feigenbaum scenario.

Keywords: recurrence equation, Ricker model, periodic Malthusian parameter, stability, bifurcation, multistability

Funding Agency Grant Number
Russian Foundation for Basic Research 15-29-02658 офи_м


DOI: https://doi.org/10.20537/nd1604001

Full text: PDF file (317 kB)
References: PDF file   HTML file

UDC: 517.9
MSC: 37G35
Received: 07.06.2016
Accepted:22.09.2016

Citation: K. V. Shlufman, G. P. Neverova, E. Ya. Frisman, “Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability”, Nelin. Dinam., 12:4 (2016), 553–565

Citation in format AMSBIB
\Bibitem{ShlNevFri16}
\by K.~V.~Shlufman, G.~P.~Neverova, E.~Ya.~Frisman
\paper Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 4
\pages 553--565
\mathnet{http://mi.mathnet.ru/nd537}
\crossref{https://doi.org/10.20537/nd1604001}
\elib{http://elibrary.ru/item.asp?id=27715762}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. V. Shlyufman, G. P. Neverova, E. Ya. Frisman, “Dinamicheskie rezhimy modeli Rikera s periodicheski izmenyayuschimsya maltuzianskim parametrom”, Nelineinaya dinam., 13:3 (2017), 363–380  mathnet  crossref  elib
    2. L. S. Ibragimova, M. G. Yumagulov, A. R. Ishbirdin, M. M. Ishmuratova, “Matematicheskoe modelirovanie dinamiki chislennosti biologicheskoi populyatsii pri izmenyayuschikhsya vneshnikh usloviyakh na primere burzyanskoi bortevoi pchely (Apis mellifera L., 1758)”, Matem. biologiya i bioinform., 12:1 (2017), 224–236  mathnet  crossref
    3. 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  mathnet  crossref
    4. 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  mathnet  crossref
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