Asymptotic analysis of a model of steady state of a biocoenosis
The author gives a quite detailed analysis of the so-called ``stationary state model'' for biocoenosis of some competing populations. The main results include the construction of an asymptotic representation for the solution of the model, described by the aid of some integro-differential equations. Using some results of \textit{J. M. Cushing} [J. Math. Biol. 20, 259-276 (1984; Zbl 0553.92014)] and \textit{M. I. Stronyna} [Mathematical analysis of a class of models of the dynamics of biological populations. Russian preprint (1981)] he proves two theorems which furnish finally the required asymptotic solutions and also an estimate of the error implied by the derived solutions. The author also studies the behaviour of the solutions and examines some peculiar ones which might be of interest for biomathematicians. A final remark is that the potential readers of this article must be well up concerning dynamic models for ecological systems.
scientific article; zbMATH DE number 4029343