Dynamics of predator–prey models with a strong Allee effect on the prey and predator-dependent trophic functions

Bifurcations of a Leslie Gower predator prey model with Holling type III functional response and Michaelis-Menten prey harvesting

“…The roots of f (x) are x ± from (7), it is not difficult to show that f (x) takes positive values in the first quadrant if and only if the roots x ± are not equal and at least one of them is positive. Using this analysis, we conclude that positive non-trivial equilibria points exist only in one of the following three areas (see figure (2) ):…”

“…is the Holling type III functional response. To have a biologically meaningful interpretation we need p(x) > 0 (see [2]), thus b > −2 √ a (then, ax 2 + bx + 1 = 0 is positive for all x ≥ 0). Based on the work of [5] and [8] we propose a model with same assumptions as model (1), but with functional response of Holling type III.…”

Coexistence in seasonally varying predator–prey systems with Allee effect

“…Remark 1. With these general assumptions, which are satisfied by functions reported in [6,7], k is suitable to model a weak and a strong Allee effect on the prey growth. In [6,7] other technical assumptions on the prey growth were considered, which involve the first and the second derivatives of k (with respect to N ), in order to perform the existence and stability analysis of equilibrium states.…”

“…The Allee effect can be weak or strong, depending on the sign of prey growth function (non-negative or negative, respectively) for small population abundance. Autonomous predator-prey models with Allee effect in the prey are largely analyzed in literature [6,7,20,48,52], the analogous problem for seasonally dependent models was, as far as we know, less studied.…”

Dynamical analysis of an integrated pest management predator–prey model with weak Allee effect

“…The Allee effect is a phenomenon in biology characterized by a correlation between population size or density and the mean individual fitness (often measured as per capita population growth rate) of a population or species [11,15,17]. Many scholars investigated the rich dynamical behaviours of predator-prey model with Allee effect [1,7,16,18,21,24,34,40,44,45,48]. To consider that the predators are difficult to seek spouses when the species has a low population density, the Allee effect on predator is introduced to model phenomenon.…”