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Matem. Mod., 2007, Volume 19, Number 6, Pages 3–15 (Mi mm975)  

Using the channels and jokers method for the Rosenzweig–Macarthur system dynamics description

M.-G. M. Zulpukarov, G. G. Malinetskii, A. V. Podlazov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: Nowadays, methods of nonlinear dynamics and asymptotical analysis are widely used in biological systems research. This article reviews the Rosenzweig–Macarthur system, a model of the simple biological system (a tritrophic food chain). This system is remarkable for the multiplicity of its dynamical modes. A new technique of the numerical modeling, the channels and jokers method, is used. The latter method is based on detection (by means of asymptotical analysis) of regions with wide horizon of predictability and small number of essential variables (which regions are called channels), and regions of poor predictability (jokers). Then, distinct numerical modelling algorithms are used for channels and jokers separately. It is shown, that the technique proposed lets obtain both good quantitative and qualitative idea of the model dynamics.

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Received: 29.05.2006

Citation: M.-G. M. Zulpukarov, G. G. Malinetskii, A. V. Podlazov, “Using the channels and jokers method for the Rosenzweig–Macarthur system dynamics description”, Matem. Mod., 19:6 (2007), 3–15

Citation in format AMSBIB
\Bibitem{ZulMalPod07}
\by M.-G.~M.~Zulpukarov, G.~G.~Malinetskii, A.~V.~Podlazov
\paper Using the channels and jokers method for the Rosenzweig--Macarthur system dynamics description
\jour Matem. Mod.
\yr 2007
\vol 19
\issue 6
\pages 3--15
\mathnet{http://mi.mathnet.ru/mm975}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2423985}
\zmath{https://zbmath.org/?q=an:1137.37311}


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