Dynamics of a Diffusive Predator–prey Model With Additive Allee Effect

Abstract

In this paper, we investigate the dynamics of a diffusive predator-prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator-prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator-prey system.

Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

“…Implementing Cardan's method as performed by Cai et al [7], we obtain the existence of the positive equilibria as follows.…”

“…Allee effect may occur under several mechanisms, such as difficulties in finding mates when population density is low or social dysfunction at small population sizes. When such a mechanism operates, the per capita fertility rate of the species increases with density; that is, positive interaction among species occurs [5][6][7][8]. Recently Indrajaya et al [9] investigate a modified Leslie-Gower equation with Beddington-DeAngelis functional response and additive (both weak and strong) Allee effect on prey…”

Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth

“…Segel and Jackson [4] first used reaction-diffusion system to explain pattern formation in ecological context based upon the seminal work by Turing [3]. Since then, a lot of studies have been devoted to spatiotemporal patterns which were produced by reactiondiffusion predator-prey, models with either a prey-dependent or a ratio-dependent predator functional response, for example, [1,2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references cited therein.…”

Positive steady states of a density-dependent predator-prey model with diffusion

“…In [5], the authors established the following model with Allee effect (measured by the term m N + b ):…”

“…and investigated the asymptotical stability of the positive equilibrium, and gave the conditions of the existence of the Hopf bifurcation. Furthermore, in [6], based on the results in [5], the authors investigated the effect of density-dependent death rate…”