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Model. Anal. Inform. Sist., 2013, Volume 20, Number 5, Pages 5–24 (Mi mais329)  

Relaxation Oscillations in Models of Multi-Species Biocenose

S. A. Kaschenko

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: Some families of mathematical models of biological populations are considered. Invariant ratios between the parameters which characterize this or that population are revealed. Dynamic properties of models are investigated on the assumption that one or several populations are strongly prolific, which means that the corresponding malthusian coefficients are rather great. On the basis of a special asymptotic method developed by the author a problem of behavior of initial system solutions can be reduced to a significantly simpler problem of dynamics of the finite-dimensional mappings received. In particular, it is shown that irregular relaxation vibrations are typical for the solutions of these mappings and, as a result, for the solution of the initial equation systems. It is interesting to note that these viabrations are of big amplitudes.

Keywords: relaxation oscillations, large parameter, asymptotic behavior, periodic solution.

Full text: PDF file (488 kB)
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UDC: 517.9
Received: 01.08.2013

Citation: S. A. Kaschenko, “Relaxation Oscillations in Models of Multi-Species Biocenose”, Model. Anal. Inform. Sist., 20:5 (2013), 5–24

Citation in format AMSBIB
\Bibitem{Kas13}
\by S.~A.~Kaschenko
\paper Relaxation Oscillations in Models of Multi-Species Biocenose
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 5
\pages 5--24
\mathnet{http://mi.mathnet.ru/mais329}


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