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The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per-capita growth rate at low densities is reduced. We examine…

Statistical Mechanics · Physics 2011-04-12 Michael T. Gastner , Beata Oborny , Alexey B. Ryabov , Bernd Blasius

We study a stochastic lattice predator-prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained…

Statistical Mechanics · Physics 2007-05-23 M. J. Washenberger , M. Mobilia , U. C. Tauber

In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…

Pattern Formation and Solitons · Physics 2020-10-30 Debaldev Jana , Saikat Batabyal , M. Lakshmanan

Diffusion-driven instability and bifurcation analysis are studied in a predator-prey model with herd behavior and quadratic mortality by incorporating multiple Allee effect into prey species. The existence and stability of the equilibria of…

Dynamical Systems · Mathematics 2023-08-17 Jianglong Xiao , Yonghui Xia

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the…

Populations and Evolution · Quantitative Biology 2019-03-06 Jozsef Z. Farkas , Andrew Yu Morozov , E. G. Arashkevich , A. Nikishina

In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the…

Analysis of PDEs · Mathematics 2023-01-05 Qi Wang

We study a predator-prey system with a generalist Leslie-Gower predator, a functional Holling type II response, and a weak Allee effect on the prey. The prey's population often grows much faster than its predator, allowing us to introduce a…

Dynamical Systems · Mathematics 2025-03-06 Roberto Albarran García , Martha Alvarez-Ramírez , Hildeberto Jardón-Kojakhmetov

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium…

Dynamical Systems · Mathematics 2025-04-03 Jianhang Xie , Changrong Zhu

In contrast to the neutral population cycles of the deterministic mean-field Lotka--Volterra rate equations, including spatial structure and stochastic noise in models for predator-prey interactions yields complex spatio-temporal structures…

Populations and Evolution · Quantitative Biology 2013-10-16 Ulrich Dobramysl , Uwe C. Tauber

A predator-prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium point in the first…

Dynamical Systems · Mathematics 2020-09-10 Claudio Arancibia-Ibarra , Jos/'e Flores

This paper investigates the dynamical behaviors of a Holling type I Leslie-Gower predator-prey model where the predator exhibits an Allee effect and is subjected to constant harvesting. The model demonstrates three types of equilibrium…

Dynamical Systems · Mathematics 2025-04-02 Jianhang Xie , Changrong Zhu

The Allee effect is an important phenomenon in population biology characterized by positive density dependence, that is a positive correlation between population density and individual fitness. However, the effect is not well studied in…

Analysis of PDEs · Mathematics 2015-10-20 Rana D. Parshad , Emmanuel Quansah , Kelly Black , Nitu Kumari , Ranjit K. Upadhyay , S. K. Tiwari

In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates…

Dynamical Systems · Mathematics 2022-11-02 Susmita Sadhu

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic…

Populations and Evolution · Quantitative Biology 2011-09-20 Uwe C. Tauber

We study the influence of spatially varying reaction rates on a spatial stochastic two-species Lotka-Volterra lattice model for predator-prey interactions using two-dimensional Monte Carlo simulations. The effects of this quenched…

Statistical Mechanics · Physics 2008-12-18 Ulrich Dobramysl , Uwe C. Tauber

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…

Populations and Evolution · Quantitative Biology 2015-06-26 Kelly C. de Carvalho , Tania Tome

We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or…

Probability · Mathematics 2012-05-15 Davide Borrello

We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…

Analysis of PDEs · Mathematics 2021-05-10 Wonhyung Choi , Thomas Giletti , Jong-Shenq Guo

Apparent competition is an indirect interaction between species that share natural resources without any mutual aggression but negatively affect each other if there is a common enemy. The negative results of the apparent competition are…

Populations and Evolution · Quantitative Biology 2022-02-16 J. Menezes , B. Moura

Predator-prey models in theoretical ecology have a long and complex history, spanning decades of research. Most of the models rely upon simple reproduction and mortality rates associated with different types of functional responses. A key…

Populations and Evolution · Quantitative Biology 2025-03-04 Tanmay Das , Mahatsab Mandal