title: Bifurcations and dynamics of a discrete predator-prey system.
abstract: In this paper, we study the dynamics behaviour of a stratum of plant-herbivore which is modelled through the following F(x, y)=(f(x, y), g(x, y)) two-dimensional map with four parameters defined by [Formula: see text] where x ≥ 0, y ≥ 0, and the real parameters a, b, r, k are all positive. We will focus on the case a ≠ b. We study the stability of fixed points and do the analysis of the period-doubling and the Neimark-Sacker bifurcations in a standard way.
authors: a Department of Mathematical Sciences , Isfahan University of Technology , Isfahan 84156 , Iran.
authors: Rasoul
authors: R
authors: Asheghi
mesh_terms: D000818:Animals; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D010507:Periodicity; D011235:Predatory Behavior / Q000502:physiology*
keywords: 34K20; 92C50; 92D25; Neimark–Sacker and period-doubling bifurcation; dynamics; host–parasite model; plant–herbivore model; predator–prey system