The dynamics of the planar two-species Lotka-Volterra predator-prey model are well-understood. Onto such a predator-prey model, we introduce a third species, a scavenger of the prey. Our model allows for two scenarios, one where the scavenger is also a predator of the original prey, and one where the presence of the scavenger simply inhibits the prey. We show all trajectories are bounded in for...

The dynamics of the classic planar two-species Lotka-Volterra predator-prey model are well understood. We introduce a scavenger species, who scavenges the predator and is also a predator of the common prey. For this model, we analytically prove that all trajectories are bounded in forward time, and numerically demonstrate persistent bounded paired cascades of period-doubling orbits over a wide ...

In this paper, we presented a predator–prey model with spatial diffusion and densitydependent noise. It was found that the spatial model without noise has spotted pattern. However, combined with density-dependent noise, the predator–prey model exhibits transition from spotted to labyrinth pattern. Furthermore, when noise intensity and temporal correlation are in appropriate levels, the populati...

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model. Keywords— Predator-prey model, Holling II type functional response, Positive periodic solution, Coincidence degree theorem

A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with BeddingtonDeAngelis functional responses is proposed. By using Gaines andMawhin’s continuation theorem of coincidence degree theory, ...

A new species, Agistemus aimogastaensis, is described with the aid of optical and Scanning Electron Microscopy. This mite is an important predator of two eriophyid mites (Aceria oleae and Oxycenus maxwelli) in olive orchards (Olea europaea, variety Arauco) in La Rioja Province. The problems related to eriophyids in olive orchards in Argentina are highlighted and photos of the damage on leaves a...

A delayed Lotka–Volterra type predator–prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to prey. By analyzing characteristic equations and...

Parameter estimation for the functional response of predator-prey systems is a critical methodological problem in population ecology. In this paper we consider a stochastic predator-prey system with non-linear Ivlev functional response and propose a method for model parameter estimation based on time series of field data. We tackle the problem of parameter estimation using a Bayesian approach r...

In this paper we build a prey-predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two...

A delayed periodic ratio-dependent predator–prey model with prey dispersal and stage structure for predator is investigated. It is assumed that immature individuals and mature individuals of the predator species are divided by a fixed age, and that immature predators don!t have the ability to attack prey, and that predator species is confined to one of the patches while the prey species can dis...