Geodesic
Relaxation Oscillations in Models of Multi-Species Biocenose
Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 5-24

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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.
Mots-clés : relaxation oscillations
Keywords: large parameter, asymptotic behavior, periodic solution. 
@article{MAIS_2013_20_5_a0,
     author = {S. A. Kaschenko},
     title = {Relaxation {Oscillations} in {Models} of {Multi-Species} {Biocenose}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {5--24},
     publisher = {mathdoc},
     volume = {20},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a0/}
}
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S. A. Kaschenko. Relaxation Oscillations in Models of Multi-Species Biocenose. Modelirovanie i analiz informacionnyh sistem, Tome 20 (2013) no. 5, pp. 5-24. http://geodesic.mathdoc.fr/item/MAIS_2013_20_5_a0/