Authors A.B. Chernyshov, O.I. Atroschenko
Month, Year 04, 2016 @en
Index UDC 681.51
Abstract We consider the important independent task of applying the method of analytical design of aggregated regulators on the set of invariant manifolds synergetic synergetic control theory to the synthesis of control laws of population processes in the ecological system of the «predator-prey», described by models of Volterra-Lotka. Ecological model of the «predator-prey» describes the dynamics of populations in the ecological system. The task of managing the dynamics of populations is the synthesis of control laws that maintain the specified number of victims or predators and reflect the natural character of their behavior. The essence of the synergistic approach to management theory is self-directed dynamic systems by artificially constructing attractors in their phase space. Enter the desired invariant manifolds (macro variables) – Environmental attractors in accordance with the purpose of managing, which attracts all trajectories of the system. The equations of motion of the system that determine the dynamics on the invariant manifold – the desired number of prey populations. A program in the software package Maple 2015.0, allowing to simulate the closed-loop control, graphs obtained transients closed systems built phase trajectories, the representative points which, starting from an arbitrary initial conditions fall on the invariant manifold. Analytically synthesized control laws that transform systems on a prescribed invariant manifolds for models of the «predator-prey».

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Keywords Volterra-Lotka model; system «predator–prey»; synthesis; control law; attractor; phase portrait; control system
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