Multiple periodic solutions of an impulsive predator–prey model with Holling-type IV functional response

Multiple Positive Periodic Solutions of a Discrete Time Delayed Predator–Prey System with Harvesting Terms

“…Moreover, we always assume that all of the parameters are positive constant. Since many authors [3][4][5][6] have argued that the discrete time models governed by difference equations are more appropriate than the continuous ones when the populations have non-overlapping generations, also, since discrete time models can also provide efficient computational models of continuous models for numerical simulations, it is reasonable to study discrete time predator-prey system with harvesting terms governed by difference equations. One of the way of deriving difference equations modelling the dynamics of populations with non-overlapping generations is based on appropriate modifications of the corresponding models with overlapping generations [7,8].…”

Dynamics of a Diffusive Modified Leslie-Gower with Holling Type IV

“…Further, Aziz-Alaoui et al [8] investigated a predator-prey system with a modified version of Leslie-Gower and Holling type II schemes. Meanwhile, the traits of non-monotonic Holling type IV functional response have been clearly recognized and it is widely used to describe the process of predation with self-selection and the inhibitory effect of prey in the recent years [8][9][10][11][12]. Thus, we consider a diffusive modified Leslie-Gower with Holling type IV schemes, which can be described as following: 1 c is the maximum value of the per capita reduction of H due to P , 2 2 / c a measures the ration of prey to support one predator, 1 e is interpreted as the half-saturation constant, 2 e indicates the quality of the alternative that provides the environment, ∆ is the Laplacian operator, 1 d and 2 d are diffusion coefficient.…”

A New Existence Theory for Positive Periodic Solutions to a Class of Neutral Delay Model with Feedback Control and Impulse

“…These perturbations bring sudden changes to the system. Systems with such sudden perturbations involving impulsive differential equations have attracted the interest of many researchers in the past twenty years, see [12][13][14][24][25][26][27][28][29][30], since they provide a natural description of several real processes subject to certain perturbations whose duration is negligible in comparison with the duration of the process. Such processes are often investigated in various fields of science and technology such as physics, population dynamics, ecology, biological systems, and optimal control.…”