English
Related papers

Related papers: Coexistence Steady States in a Predator-Prey Model

200 papers

We analyse a modified Holling-Tanner predator-prey model where the predation functional response is of Holling type II and we incorporate a strong Allee effect associated with the prey species production. The analysis complements results of…

Dynamical Systems · Mathematics 2019-10-23 Claudio Arancibia-Ibarra , Jose D. Flores , Graeme J. Pettet , Peter van Heijster

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the…

Analysis of PDEs · Mathematics 2019-07-05 Hai-Yang Jin , Zhi-An Wang

The theory of backward bifurcations provides a criterion for the existence of positive steady states in epidemiological models with parameters where the basic reproductive ratio is less than one. It is often seen in simulations that this…

Dynamical Systems · Mathematics 2025-10-22 Alexis Nangue , Alan D. Rendall

We consider the local bifurcation and global dynamics of a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, heteroclinic cycle at a threshold of…

Dynamical Systems · Mathematics 2020-07-28 Yanfei Du , Ben Niu , Junjie Wei

Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…

Dynamical Systems · Mathematics 2019-01-23 Tobia Dondè

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

Analysis of PDEs · Mathematics 2023-12-19 Francisco J. Vielma-Leal , Miguel A. D. R. Palma , Miguel Montenegro-Concha

This work analyzes a predator-prey cross-diffusion system coupled with two chemical substances under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R^n (n >= 2) with smooth boundary dOmega. Under appropriate…

Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species…

Populations and Evolution · Quantitative Biology 2015-10-13 Aladeen Basheer , Emmanuel Quansah , Schuman Bhowmick , Rana D. Parshad

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

Groups in ecology are often affected by sudden environmental perturbations. Parameters of stochastic models are often imprecise due to various uncertainties. In this paper, we formulate a stochastic Holling II one-predator two-prey system…

Probability · Mathematics 2020-06-29 Fei Sun

The diffusive Beddington-DeAngelis predator-prey model with nonlinear prey-taxis and free boundary is considered. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behavior of the global solution.…

Analysis of PDEs · Mathematics 2018-11-14 Jianping Wang , Mingxin Wang

Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a…

Analysis of PDEs · Mathematics 2009-07-08 Christoph Walker

In this work we study the permanence and extinction of a regime-switching predator-prey model with Beddington-DeAngelis functional response. The switching process is used to describe the random changing of corresponding parameters such as…

Probability · Mathematics 2020-01-14 Jianhai Bao , Jinghai Shao

A non-Markovian stochastic predator-prey model is introduced in which the prey are immobile plants and predators are diffusing herbivors. The model is studied by both mean-field approximation (MFA)and computer simulations. The MFA results a…

Disordered Systems and Neural Networks · Physics 2009-10-31 Rouzbeh Gerami , Mohammad R. Ejtehadi

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

Dynamical Systems · Mathematics 2026-03-05 Wolfgang Hoegele

The paper is concerned with a system consisting of two coupled nonlinear parabolic equations with a cross-diffusion term, where the solutions at positive times define the initial states. The equations arise as steady state equations of an…

Analysis of PDEs · Mathematics 2010-11-16 Christoph Walker

A new model to investigate environmental effects of genetically distinguishable predators is presented. The Holling type II response function, modelling feeding satiation, leads to persistent system's oscillations, as in classical…

Dynamical Systems · Mathematics 2014-03-19 Clara Viberti , Ezio Venturino

In this paper, we focus on a spatial Holling-type IV predator-prey model which contains some important factors, such as diffusion, noise (random fluctuations) and external periodic forcing. By a brief stability and bifurcation analysis, we…

Populations and Evolution · Quantitative Biology 2008-01-29 Lei Zhang , Weiming Wang , Yakui Xue , Zhen Jin

A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium…

Analysis of PDEs · Mathematics 2010-02-10 Christoph Walker

Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the…

Dynamical Systems · Mathematics 2021-09-13 Kwadwo Antwi-Fordjour , Rana D. Parshad , Matthew A. Beauregard