Complicated Oscillations in the Problem of the Competition of Species

Some families of mathematical models of biological populations competing for common food are considered. Dynamic properties of these models are investigated on an assumption that one or several populations are strongly prolific, which means that the corresponding malthusian coefficients are rather large. On the basis of a special asymptotic method a problem of behavior of the initial system solutions can be reduced to a significantly simpler problem of dynamics of the finite-dimensional mappings. In particular, it has been 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 vibrations are of large amplitudes.