For citation:
Shlufman K. V., Fishman B. E., Frisman E. Y. Features of modes for one-dimensional model of ricker. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 2, pp. 12-28. DOI: 10.18500/0869-6632-2012-20-2-12-28
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language:
Russian
Article type:
Article
UDC:
517.938; 530.182
Features of modes for one-dimensional model of ricker
Autors:
Shlufman Konstantin Vladimirovich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Fishman Boris Entilevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Frisman Efim Yakovlevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Abstract:
In this paper we make investigation of aperiodic modes Ricker’s model. It’s identified two qualitatively different kinds of aperiodic modes for this model. It’s defined one of the selected types of aperiodic modes. We have called him interval time-periodic mode. For analyze of dynamics of one-dimensional system we used pseudo phase space with a big lag. The maps of the interval of periodic modes are made. We discuss the distribution of interval periodic modes into parameter space of Ricker’s model.
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Reference:
- Kuznetsov SP. Dynamical Chaos: Course of Lectures. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
- Ricker WE. Computation and interpretation of biological statistics of fish populations. Ottawa: Bulletin of the Fisheries Research Board of Canada, Bulletin 191; 1975.
- Ashikhmina EV, Israelsky YuG, Frisman EYa. Dynamics of the Ricker model with periodical parameter variation. Bulletin of the Far Eastern Branch of the Russian Academy of Sciences. 2004;5:19–28 (in Russian).
- Gromova NP. Equilibrium and oscillatory limit regimes in models of two competing populations with discrete time. Mathematical studies in population ecology. Bulletin of the Far Eastern Branch of the Russian Academy of Sciences. 1988;107 (in Russian).
- Skaletskaya EI, Frisman EYa, Shapiro AP. Discrete models of population dynamics and harvest optimization. Moscow: Nauka; 1979. 165 p. (in Russian).
- Schuster G. Deterministic Chaos. An Introduction. Moscow: Mir; 1988. 240 p. (in Russian).
- Yakobson MV. On the properties of dynamical systems generated by mappings of the form x → Axe−bx. Modeling of biological communities. Vladivostok: Far Eastern Scientific Center of the USSR Academy of Sciences. 1975:141–162 (in Russian).
- Skorokhod AV. Probability. Basic concepts. Structure. Methods. Itogi Nauki i Tekhniki. Series: Sovrem. Probl. Mat. Fund. Napr. Moscow: VINITI. 1989;43:5–145 (in Russian).
- Shapiro AP, Luppov SP. Recurrent equations in the theory of population biology. Moscow: Nauka; 1983. 133 p. (in Russian).
Received:
12.05.2011
Accepted:
22.03.2012
Published:
29.06.2012
Journal issue:
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