Bifurcation and Chaotic Behavior of a Nonlinear Discrete Fractional Order Prey-Predator System

The present work investigates discrete form of fractional order prey-predator interactions obtained from its continuous model by the process of discretization. Mathematically the dynamics of this system is analyzed such as the existence of non-negative fixed points, local stability of the axial and interior fixed points. Jury conditions are applied to illustrate stability of the axial and interior fixed points. Phase portraits, bifurcation figures, chaotic attractors and time plots are showcased for diverse set of parametric values. The sensitive dependence on initial conditions of the parameter values for the axial and interior fixed points are discussed.