Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses

Analysis of a Lévy-diffusion Leslie-Gower predator-prey model with nonmonotonic functional response

“…The concept of the functional response was first introduced by Solomon (1949). The carrying capacity of the predator's environment is assumed to be proportional to the prey abundance, i.e., (x+k 2 )/h, which is called as a modified Leslie-Grower term [2]. The functional response p(x) has been developed during various different processes of energy transfer (see [35]).…”

“…For simplicity, we apply the following transformation to the variables and the parameters in the system (3) x = k 1 u, y = v/k 1 , ak 2 1 =ā, bk 1 =b, τ = k 1 t, s 2 k 1 = η, r = h/k 2 1 , k 2 /k 1 = k, and we still use a, b to stand forā,b. Thus (3) becomes the following form:…”

Positive solutions for a modified Leslie–Gower prey–predator model with Crowley–Martin functional responses

“…By take above considerations, Ali and Jazar [2] consider a prey-predator model which incorporates a modified version of the Leslie type functional response parameters, in which c measures the magnitude of interference among prey. Further, a 2 describes the growth rate of predator v; e is the maximum value which per capita reduction rate of v can attain, f measure the extent to which environment provides protection to predator v.…”

Persistence and extinction of a stochastic predator–prey model with modified Leslie–Gower and Holling-type II schemes

“…a means the intraspecific competition strength, c measures the per capita reduction rate, h characterises the safeguard of the environment and f possesses the like signification of c. In the past two decades, model (1) and its generalisations have been subjected to intensive research, and a mass of attractive features have been provided. For example, Aziz-Alaoui and Okiye [1] tested the boundedness and global stability of model (1); Guo and Song [2] dissected model (1) perturbed by the impulse; Abid et al [3] probed into the optimal control of model (1); see [3][4][5][6][7][8][9][10][11][12][13][14][15] for more related outcomes. The parameters in model (1) are hypothesised to be deterministic, which neglects the environmental perturbations, and hence model (1) cannot accurately depict the real situations.…”