Extending the Range of Stability for the Periodic Orbits of a Prey – Predator Chaotic System

Some dynamical systems with biological significance are well described by mappings depending sensitively on one or more parameters. The environment fluctuations can change these parameters and, along with them, the desired behavior of the system. In order to maintain a fixed activity, a number of control approaches have been proposed. In the paper, extensive computer simulations have been provided to show the effectiveness of a technique suggested by N.A. Magnitskii in locating and stabilizing the unstable periodic orbits (UPOS) of multidimensional chaotic mappings. The method is illustrated through the example of a two-dimensional preypredator chaotic system.