Related papers: Prey-Predator models on graphs
This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.
In this paper, we proposed a population model depicting the dynamics of a prey species showing group defence against a generalist predator. The group defence characteristic is represented by a non-monotonic functional response. We have…
This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…
In this paper, we study in detail the structure of the global attractor for the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in [19] and prove that its…
For a stationary system representing prey and $N$ groups of competing predators, we show classification results about the set of positive solutions. In particular, we show that if the number of components $N$ is too large or if the…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are…
The time-global unique solvability on the reaction diffusion equations for prey-predator models with density-dependent inhibitor and dormancy on predators is established. The crucial step of the proof is to construct time-local non-negative…
In this paper, we consider a two species chemotaxis system of parabolic-parabolic-elliptic type with Lotka-Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global…
Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in…
This paper aims to introduce a concept of an equilibrium point of a dynamical system which will call it almost global asymptotically stable. A biological prey-predator model is also analyzed with a modification function growth in prey…
In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
This paper is devoted to the mathematical analysis of a nonlinear stochastic reaction-diffusion system modeling predator-prey interactions with prey-taxis and noises. Precisely, we detail the proof of the existence of weak martingale…
We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type II functional response studied by M.A. Aziz-Alaoui and M. Daher-Okiye. The modification consists in incorporating a refuge for preys, and…
We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
The Lotka-Volterra model reflects real ecological interactions where species compete for limited resources, potentially leading to coexistence, dominance of one species, or extinction of another. Comprehending the mechanisms governing these…
We study communities emerging from generalised random Lotka--Volterra dynamics with a large number of species with interactions determined by the degree of niche overlap. Each species is endowed with a number of traits, and competition…
In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its…
This paper investigates a class of chemotaxis systems modeling lethal interactions in a smooth, bounded domain $\Omega \subset \mathbb{R}^n$ with homogeneous Neumann boundary conditions. We examine two distinct cases: (i) a fully parabolic…