The problem of finding optimal trajectories for a controlled population model that takes into account competition and migration

A three-dimensional controlled model of population dynamics taking into account competition and migration is studied. The control quality criterion for this model is considered within the framework of the optimal control problem with phase constraints. Computer research of a nonlinear model with competition and migration made it possible to obtain the results of numerical experiments on the finding for control laws, a criterion for the quality of control, and optimal trajectories. Symbolic computation algorithms are used to solve optimal control problems. These algorithms are based on the use of heuristic methods of numerical optimization in combination with methods for generating control functions. A comparative analysis of the results for various degrees of polynomials, in the form of which the finding for control functions is carried out, is performed. As a tool for solving the problem of optimal control and researching the model, a software package developed with the help of Python libraries is used.