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Volume 57 >>> № 2 MARCH — APRIL 2021

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UDC 519.8

S.V. Pashko¹

¹ Institute of Software Systems,
National Academy of Sciences of Ukraine, Kyiv, Ukraine

TIME OPTIMAL CONTROL PROBLEM FOR THE LOTKA–VOLTERRA SYSTEM

Abstract. We consider a controlled system of Lotka–Volterra differential equations that describes the evolution of two interrelated populations of predators and prey. The system contains two control variables, which are chosen so that the transition time to a stationary point is minimal. In the article, the control functions and the corresponding trajectories of motion in the state space are constructed, and their optimality is substantiated.

Keywords: maximum principle, stationary point, minimum time.

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