We consider a predator-prey model, where some prey are completely free from predation within temporal or spacial refuge and the predator population is subject to Allee effect. study effect of presence on stability bifurcation system. investigate existence model as well region. also obtain invariant manifolds

The objective of this paper is to investigate the effect of prey-taxis on predator–prey models with Paramecium aurelia as the prey and Didinium nasutum as its predator. The logistic Lotka–Volterra predator–prey models with prey-taxis are solved numerically with four different response functions, two initial conditions and one data set. Routh–Hurwitz’s stability conditions are used to obtain the...

We have constructed a synthetic ecosystem consisting of two Escherichia coli populations, which communicate bi-directionally through quorum sensing and regulate each other's gene expression and survival via engineered gene circuits. Our synthetic ecosystem resembles canonical predator-prey systems in terms of logic and dynamics. The predator cells kill the prey by inducing expression of a kille...

study of the spatial distribution of a pest and its natural enemies provides better decision tool for integrated pest management. the spatial distribution and seasonal activity of panonychus ulmi (koch) and its predator zetzellia mali (ewing) were studied in an apple orchard in khoramdareh (zanjan province, iran) during 2007. the interaction (density dependence) between the prey and its predato...

A stochastic version of the classical predatorprey population model is considered through a simple birthdeath formulation. The expected value of the process is obtained and shown to correspond to the deterministic predatorprey population model.

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It assumed that the rate at which moves density. The fixed points, their local stability, and existence of Neimark-Sacker bifurcation are investigated. At last, numerical simulations consisting diagrams, phase portraits, time-series given support analytical findings. occurrence ...

In this paper, a asymptotically periodic predator-prey model with Modified Leslie-Gower and Holling-Type II schemes is investigated. Some sufficient conditions for the uniformly strong persistence of the system are established. Our result is an important complementarity to the earlier results. Keywords—Predator-prey model, uniformly strong persistence, asymptotically periodic, Holling-type II.

Predators can affect prey populations and, via trophic cascades, predators can indirectly impact resource populations (2 trophic levels below the predator) through consumption of prey (density-mediated indirect effects; DMIEs) and by inducing predator-avoidance behavior in prey (trait-mediated indirect effects; TMIEs). Prey often employ multiple predator-avoidance behaviors, such as dispersal o...

A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a parametric analysis of stability properties of dynamics on the system in which the functional response is a function of the ratio of prey to predator. It is shown that incorporating of Allee effect on prey equation significantly modifies the dynamics of the original system, as the modified model invol...

Predator-prey systems have been studied extensively. See, for instance, [1, 6, 8–10] and the references cited therein. Most of the previous papers focused on the predator-prey systems without stocking. Brauer and Soudack [2, 3] studied some predator-prey systems under constant rate stocking. To our knowledge, few papers have been published on the existence of positive periodic solutions for del...