ANALYZING THE PHASE PATHS WHILE MODELING THE “PREDATORPREY” SYSTEM DYNAMICS

The contribution paper analyses the phase paths in an ecological “predator-prey” system while modeling the dynamics of interactions between populations with the real parameters for Zhytomyr region. When evaluated at the steady state the ecological system showed probable disturbances of equilibrium with eventual transition to the chaotic state. The conclusions are made about equilibrium points, which are determined by the Jacobian eigenvalues. The chaotic dynamics feasibly requires control to avoid the ecosystem downturns and the possible damage. The research showed an adequate reproduction of the "predator-prey" process. It is described by mathematical models on the basis of a generalized model of system evolution, in contrast to models based on the Verhulst function