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Matematicheskaya Biologiya i Bioinformatika, 2020, Volume 15, Issue 1, Pages 73–92
DOI: https://doi.org/10.17537/2020.15.73
(Mi mbb423)
 

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Modeling

Dynamics of predator-prey community with age structures and its changing due to harvesting

G. P. Neverovaa, O. L. Zhdanovaa, E. Ya. Frismanb

a Institute for Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok, Russia
b Regional Problems Complex Analysis Institute of the Russian Academy of Sciences Far East Division, Birobidzhan, Russia
References:
Abstract: The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.
Key words: discrete-time mathematical model, community, predator-prey, stability, dynamic modes, age structure, harvest.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-45004 ИНД_а
Received 03.03.2020, 03.05.2020, Published 05.06.2020
Document Type: Article
Language: Russian
Citation: G. P. Neverova, O. L. Zhdanova, E. Ya. Frisman, “Dynamics of predator-prey community with age structures and its changing due to harvesting”, Mat. Biolog. Bioinform., 15:1 (2020), 73–92
Citation in format AMSBIB
\Bibitem{NevZhdFri20}
\by G.~P.~Neverova, O.~L.~Zhdanova, E.~Ya.~Frisman
\paper Dynamics of predator-prey community with age structures and its changing due to harvesting
\jour Mat. Biolog. Bioinform.
\yr 2020
\vol 15
\issue 1
\pages 73--92
\mathnet{http://mi.mathnet.ru/mbb423}
\crossref{https://doi.org/10.17537/2020.15.73}
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  • https://www.mathnet.ru/eng/mbb/v15/i1/p73
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    This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
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