Relaxation oscillations in models of multispecies biocenose

Abstract

Families of mathematical models of biological populations have been considered. Invariant ratios between the parameters characterizing various populations have been revealed. Dynamic properties of models have been investigated under the assumption that one or several populations are strongly prolific, which means that the corresponding Malthusian coefficients are rather great. Based on a special asymptotic method developed by the author, the behavior problem for solutions of the original system can be reduced to a significantly simpler problem of the dynamics of the obtained finite-dimensional mappings. In particular, it has been shown that irregular relaxation oscillations are typical of solutions of those mappings and, as a result, for solving the original system of equations. Those oscillations are of large amplitudes.