Mathematical ecology: Forecast, assessment and optimization of impacts on natural ecosystems

Abstract

Several topics are considered as illustrations for non-traditional formulations of prediction and optimization problems for a system serving as a model of an ecological object: the “chaos” problem in discrete equations for population dynamics; the problem “whether a predator can control its prey population”; the issues of stable existence of a trophic chain that has variable length depending on a resource input rate, an ecological and energetical analysis of aggregated agroecosystems. Search for appropriate stable structures turns out to make more sense for ecological systems than an exact prediction or strictly optimal choice of their dynamic trajectories.