This paper deals with a discrete-time predator–prey system with Allee effect. We obtain asymptotically stable conditions of the equilibrium points which are subject to the Allee effect. The stabilizing effect of Allee effect on prey and predator populations is studied, respectively. The Allee effect which occurs on both of predator and prey populations is also discussed by stability analysis, p...

It is known that one of important factors impacted on a predator-prey system is the functional response. Holling proposed three types of functional response functions, namely, Holling I, Holling II, and Holling III, which are all monotonously nondescending 1 . But for some predator-prey systems, when the prey density reaches a high level, the growth of predator may be inhibited; that is, to say...

In this paper we derive some results to ensure the global stability of a predator-prey system. The results cover most of the models which have been proposed in the ecological literature for predator-prey systems. The first result is very geometric and it is very easy to check from the graph of prey and predator isoclines. The second one is purely algebraic, however, it covers the defects of the...

Functional response estimation and population tracking in predator-prey systems are critical problems in ecology. In this paper we consider a stochastic predator-prey system with a Lotka-Volterra functional response and propose a particle filtering method for: (a) estimating the behavioral parameter representing the rate of effective search per predator in the functional response and (b) foreca...

The classical Holling type II functional response, describing the per capita predation as a function of prey density, was modified by Beddington and de Angelis to include interference of predators that increases with predator density and decreases the number of killed prey. In the present paper we further generalize the Beddington-de Angelis functional response, considering that all predator ac...

This paper aims to study the effect of Harvesting on predator species with time-delay on a Holling type-IV prey-predator model. Harvesting has a strong impact on the dynamic evolution of a population. Two delays are considered in the model of this paper to describe the time that juveniles of prey and predator take to mature. Dynamics of the system is studied in terms of local and Hopf bifurcati...

Though prey use a variety of information sources to assess predation risk, evolutionary cohistory with a predator could constrain information use, and nonnative prey might fail to recognize risk from a novel predator. Nonnative prey might instead use generalized risk assessment, relying on general alarm signals from injured conspecifics rather than cues from predators. I tested the influence of...

We utilized a long-term data base collected over a broad geographic range to examine predator size prey size relationships for 18 species of marine fish predators from continental shelf waters off the northeast US coast. Regression analysis was used to illustrate interspecific variation in ontogenetic patterns of prey size use, gape allometries, and ratio-based trophic niche breadths. Sizebased...

Throughout the history of ecology, the interaction between predators and their prey has received attention from ecologists. Some of the longest and most well-known data series in ecology are from predator and prey populations, and predator–prey models are among the oldest in the field. Despite these efforts, a discrepancy exists between the behavior of most models and that of natural predator a...

An optimal control problem is studied for a predator-prey system with logistic growth rate of the prey and a prey-dependent functional response of the predator. The control function has two components and signifies the rate of mixture between the individuals of the species. The form of the optimal control is determined according to Pontryagin’s maximum principle. It is bang-bang and the number ...