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Statistical models of ecological systems defined by Volterra equations. (English) Zbl 0935.92033

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
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