Discrete prey-predator model with Beddington-DeAngelis functional response: simple vs. complex dynamics - Agrawal, Tanuja (Global Journal of Mathematical Analysis, 2014)
In this paper the dynamics of a discrete-time prey-predator system is investigated in the closed first quadrant . The existence and stability of fixed points are analyzed algebraically .The conditions of existence for flip bifurcation is derived by busing center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results but also exhibit complex dynamical behaviors of the model, such as the periodic-doubling bifurcation in periods 2,4 and 8 and quasi-periodic orbits and chaotic sets. Keywords: Discrete Model, Beddington-Deangelis Functional Response, Stability, Flip Bifurcation, Center Manifold Theorem, Numerical Simulation.