Related papers: Protection zone in a diffusive predator-prey model…
The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal…
Methods for predicting the probability and timing of a species' extinction are typically based on a combination of theoretical models and empirical data, and focus on single species population dynamics. Of course, species also interact with…
A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous…
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…
Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species once determined as predators and preys, despite firm…
The use of predator-prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka-Volterra system towards more realistic descriptions of the processes of predation, reproduction…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness, and nonlocal competition. Within this replicator-mutator…
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…
In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
The steady-state phase diagram of the one-dimensional reaction-diffusion model 2A -> 3A, 2A -> 0 is studied through the non-hermitian density matrix renormalization group. In the absence of single-particle diffusion the model reduces to the…
Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet-hedging, to increase their probability of survival under stressful environmental fluctutation. In this context, the…
We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
In this paper, we introduce a two-sex controlled branching model to describe the interaction between predator and prey populations with sexual reproduction. This process is a two-type branching process, where the first type corresponds to…
In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…
Simulation of population dynamics is a central research theme in computational biology, which contributes to understanding the interactions between predators and preys. Conventional mathematical tools of this theme, however, are incapable…
Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of…
This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I…