Bounded finite-time stabilization of the prey - predator model via Korobov's controllability function

The problem of finite-time stabilization for a Leslie-Gower prey - predator system through a bounded control input is solved. We use Korobov's controllability function. The trajectory of the resulting motion is ensured for fulfilling a physical restriction that prey and predator cannot achieve negative values. For this purpose, a certain ellipse depending on given data and the equilibrium point of the considered system is constructed. Simulation results show the effectiveness of the proposed control methodology.