Related papers: A Free Boundary Problem for a Predator-prey Model …
The fast-reaction limit for reaction--diffusion systems modelling predator--prey interactions is investigated. In the considered model, predators exist in two possible states, namely searching and handling. The switching rate between these…
We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…
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…
In this paper we study the two-phase Bernoulli type free boundary problem arising from the minimization of the functional $$ J(u):=\int_{\Omega}|\nabla u|^p +\lambda_+^p\,\chi_{\{u>0\}} +\lambda_-^p\,\chi_{\{u\le 0\}}, \quad 1<p<\infty. $$…
A class of diffusion driven Free Boundary Problems is considered which is characterized by the initial onset of a phase and by an explicit kinematic condition for the evolution of the free boundary. By a domain fixing change of variables it…
We investigate the higher-dimensional forager-exploiter model with homogeneous Neumann boundary condition. The existence and uniqueness of global bounded classical solution is established for the high dimension.
We consider a modified Rosenzweig-MacArthur predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is…
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…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible…
It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…
We prove the existence of a solution to an 1-D free boundary problem which describes the propagation of disturbances of shock type, modeled by a non standard variational inequality.
We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end…
In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that when time goes to infinity, either one specie extincts while…
We develop an existence and regularity theory for solutions to a geometric free boundary problem motivated by models of tumor growth. In this setting, the tumor invades an accessible region $D$, its motion is directed along a constant…