Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response

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

“…where m, A and B are positive parameters that describe the effects of capture rate handling time and the magnitude of interference among predators, respectively, on the feeding rate (see [17,37,38,[50][51][52] for related works). 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.…”

“…Empirical evidence suggests that the spatial scale and structure of environment can influence population interactions [9]. By considering the above reasons, we consider the following reaction-diffusion equations: •ã denotes birth rate of prey, andb denotes the birth rate of predator; K is the carrying capacity of prey populationũ, e 2 represents intra-specific pressures of predator; • the termλṽ/[(1 +cũ)(1 +dṽ)] is known as Crowley-Martin interactions, in whichλ andd describe the effects of capture rate handling time andc describes the magnitude of interference among predators (see [17,37,38,[50][51][52]); • the termμṽ/(ũ+r) is a modified version of Leslie-Gower functional response, in whichμ is the maximum value which per capita reduction rate ofṽ can attain,r measure the extent to which environment provides protection to predatorṽ (see [5]). …”

Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response

“…For example, Yang studied the stability and instability of positive equilibrium in a predator-prey model with Crowley-Martin functional response and time delay [24]. Asymptotic properties of a stochastic predatorprey model with Crowley-Martin functional response were studied by Liu et al, such as global existence and stochastic boundedness of the positive solution [26]. A stagestructured predator-prey system with Crowley-Martin functional response was investigated, and the persistence of the system and global asymptotic stability of the positive equilibrium were assessed [27].…”

On the Analysis of Discrete Epidemic Models with Specific Nonlinear Incidence Rate

“…Firstly, we study a discrete SIR epidemic model (1) with specific nonlinear incidence rate βS k I k /(1 + α 1 S k + α 2 I k + α 3 S k I k ), where β, α 1 , α 2 and α 3 ≥ 0 are constants. S k is the number of susceptible at time k, whereas I k is the number of infected at time k. It is very important to note that this incidence rate becomes the bilinear incidence rate if α 1 = α 2 = α 3 = 0, the saturated incidence rate if α 1 = α 3 = 0 or α 2 = α 3 = 0, the modified saturated incidence rate proposed in [8,9] when α 3 = 0, and Crowley-Martin functional response presented in [10][11][12] if α 3 = α 1 α 2 . Secondly, this model is studied in discrete-time, is more accurate and more convenient as we explained above.…”