Method of Tangential Control of "Predator-Prey"

A researched model is actually a system of three ordinary differential equations, two of which are the Lotka-Volterra system where species of predator population are removed and the other one is a differential equation regarding trophic attractiveness of the patch. The problem of preserving diversity of biological society is solved by excluding predators. The existence of a curve dividing the multitude equal to various meanings of basic number of populations into two is proved: the points of the first are to be controlled in order to prevent predators' migration, the second set of points does not require control. Analytical and numerical researches of the curve have been conducted. A method of tangential control has been suggested as the one that allows to save the species structure of bio population on the patch. Control processes were constructed according to the suggested way, later the most effective one has been chosen with the help of numerical modelling in terms of its minimal invasion into natural processes of bio population and its expenses.

Keywords

trophic attractiveness of the patch; Lotka-Volterra system; dynamical system; control process; numerical method.

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