Allee effect in a discrete-time predator–prey system

Discrete prey-predator model with Beddington-DeAngelis functional response: simple vs. complex dynamics

“…The organization of this paper is as follows. In the second section we discuss the existence and local stability of fixed points in model (3). In the third section study the numerical simulations ,which not only illustrate our results with theoretical analysis but also exhibit complex dynamical behaviors such as the cascade periodic-doubling bifurcation inperiods 2,4 and 8 and quasi-periodic orbits and chaotic sets .In section four we give the discussion for our work.…”

“…Liu and Xiao [17], Jing and Yang [11], He and Lai [8], Hu et al [10] obtained the flip bifurcation by using the center manifold theorem and bifurcation theory. But Agiza et al [1] and Celik et al [3] only showed the flip bifurcation and Hopf bifurcation by using numerical simulations. A functional response is called of Beddington-DeAngelis type if it takes the form .…”

A nonstandard numerical scheme for a predator-prey model with Allee effect

“…Strong and weak Allee effect may be mentioned that as a result of the Allee effect has a huge impact for deterioration of biological balance and when this effect is neglected it can cause some problems. One of the most popular papers related to this effect can be read in [7,19,25,28] .…”

Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays

“…N (t) and P (t) can be interpreted as the densities of prey and predator populations at time t, respectively. Zhou et al first studied the stability conditions of the equilibrium point for the system and then by introducing so called Allee effect [3,6,7] in different forms, they investigated the impact of this effect on the dynamics of this predator-prey system. In system (1.1), there is no delay.…”