Mkhitaryan, K. N.; Pavlotskiy, I. P. Statistical models of ecological systems defined by Volterra equations. (English) Zbl 0935.92033 Math. Model. Comput. Exp. 1, No. 3, 261-272 (1993). Summary: The Vlasov equation system statistically describes the evolution of a system of interacting components. It is derived on the basis of the Verhulst-Volterra (PV) and Lotka-Volterra (LV) dynamic equations. For the Vlasov equations system the initial value problem is proved to be well posed, and the solution is shown to continuously depend on the interaction coefficients. Equations are obtained for the spread of features and for the evolution of Vlasov means, the latter coinciding with the primary dynamic equations. The Vlasov equations system is qualitatively investigated. MSC: 92D40 Ecology 37N25 Dynamical systems in biology 34C99 Qualitative theory for ordinary differential equations 34D99 Stability theory for ordinary differential equations 82B99 Equilibrium statistical mechanics PDFBibTeX XMLCite \textit{K. N. Mkhitaryan} and \textit{I. P. Pavlotskiy}, Math. Model. Comput. Exp. 1, No. 3, 261--272 (1993; Zbl 0935.92033)