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We study an one{dimensional quasilinear system proposed by J. Tello and M. Winkler [19] which models the population dynamics of two competing species attracted by the same chemical. The kinetics terms of the interacting species are chosen…

Analysis of PDEs · Mathematics 2016-11-25 Jia Hu , Qi Wang , Jingyue Yang , Lu Zhang

The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity…

Populations and Evolution · Quantitative Biology 2009-11-13 Refael Abta , Nadav M. Shnerb

In this paper we investigate a free boundary problem for the diffusive Leslie-Gower prey-predator model with double free boundaries in one space dimension. This system models the expanding of an invasive or new predator species in which the…

Analysis of PDEs · Mathematics 2017-10-27 Mingxin Wang , Qianying Zhang

This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the…

Dynamical Systems · Mathematics 2019-12-03 Aaditya Kharel , Zhifu Xie , Huiqing Zhu , Michelle McCullum , Nick Burks

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

The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…

Dynamical Systems · Mathematics 2020-02-26 Yong Yao

The method of generalized modeling has been applied successfully in many different contexts, particularly in ecology and systems biology. It can be used to analyze the stability and bifurcations of steady-state solutions. Although many…

Dynamical Systems · Mathematics 2015-03-06 Christian Kuehn , Thilo Gross

We develop a time and space dependent predator-prey model. The predators' equation is a non local hyperbolic balance law, while the diffusion of prey obeys a parabolic equation, so that predators "hunt" for prey, while prey diffuse. A…

Analysis of PDEs · Mathematics 2020-04-01 Rinaldo M. Colombo , Elena Rossi

We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To…

Statistical Mechanics · Physics 2017-10-13 Bassel Heiba , Sheng Chen , Uwe C. Täuber

This paper is concerned with the global boundedness and stability of classical solutions to an alarm-taxis system describing the burglar alarm hypothesis as an important mechanism of anti-predation behavior when species are threaten by…

Analysis of PDEs · Mathematics 2023-05-30 Hai-Yang Jin , Zhi-An Wang , Leyun Wu

The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…

Dynamical Systems · Mathematics 2024-04-23 M. N. Mooij , M. Baudena , A. S. von der Heydt , I. Kryven

We investigate the Lotka-Volterra model for predator-prey competition with a finite carrying capacity that varies periodically in time, modeling seasonal variations in nutrients or food resources. In the absence of time variability, the…

Pattern Formation and Solitons · Physics 2026-05-05 Mohamed Swailem , Alastair M. Rucklidge

In this paper we transform a continuous-time predator-prey system with general functional response and recruitment for both species into a discrete-time model by nonstandard finite difference scheme (NSFD). The NSFD model shows complete…

Numerical Analysis · Mathematics 2017-01-23 Quang A Dang , Manh Tuan Hoang

We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…

Populations and Evolution · Quantitative Biology 2025-03-20 Christian Hamster , Jorik Schaap , Peter van Heijster , Joshua Dijksman

We study a system of elliptic equations with strong competition and an arbitrary large number of components. The system is related to a model of predators and prey, with a single and where several predators compete with each other. In this…

Analysis of PDEs · Mathematics 2019-03-28 Henri Berestycki , Alessandro Zilio

In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…

Dynamical Systems · Mathematics 2019-11-20 Mary Ballyk , Ibrahim Jawarneh , Ross Staffeldt

This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…

Dynamical Systems · Mathematics 2019-05-24 Jia-Feng Cao , Wan-Tong Li , Jie Wang

In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed predator-prey planar systems in which there occurs a transcritical bifurcation of quasi steady states. The proof uses a…

Dynamical Systems · Mathematics 2016-05-25 J. Banasiak , M. S. Seuneu Tchamga

In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…

Dynamical Systems · Mathematics 2021-05-13 Lingyu Liu

In this paper we investigate two free boundary problems for a Lotka-Volterra type competition model in one space dimension. The main objective is to understand the asymptotic behavior of the two competing species spreading via a free…

Analysis of PDEs · Mathematics 2015-06-18 Mingxin Wang , Jingfu Zhao