相关论文: On impulsive reaction-diffusion models in higher d…

We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with…

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…

We develop theory to understand an intriguing property of diffusion models for image generation that we term critical windows. Empirically, it has been observed that there are narrow time intervals in sampling during which particular…

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Short et al. (Math. Mod. Meth. Appl. Sci. 18, 2008). The focus here is on the question how far a certain nonlinear…

This paper is concerned with a parabolic-parabolic-parabolic chemotaxis system with indirect signal production, modelling the impact of phenotypic heterogeneity on population aggregation \begin{equation*} \begin{cases} u_t = \Delta u -…

Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to…

In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates…

This note is motivated by the article by F. Lutscher, E. Pachepsky, and M. Lewis (2005), The Effect of Dispersal Patterns on Stream Populations SIAM Rev. Vol. 47 No. 4 pp. 749-772 on the drift paradox. We consider the case of a regime…

In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…

Let $(X_t)_{t\geq 0}$ be a regular one-dimensional diffusion that models a biological population. If one assumes that the population goes extinct in finite time it is natural to study the $Q$-process associated to $(X_t)_{t\geq 0}$. This is…

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning…

We consider a reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$, and the…

We consider a two-species chemotaxis model in $\R^d(d \ge 3)$ featuring nonlinear porous medium-type diffusion and nonlocal attractive power-law interaction. Here, the nonlinear diffusion is chosen to be $1/m_1+1/m_2=(d+2)/d$ in such a way…

This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…

In this work, we consider the spatial-temporal multi-species competition model. A mathematical model is described by a coupled system of nonlinear diffusion-reaction equations. We use a finite volume approximation with semi-implicit time…

The microscopic structure and movement of reaction fronts in reaction diffusion systems far from equilibrium are investigated. We show that some three-site interaction models exhibit exact diffusive shock measures, i.e. domains of different…

We investigate a vectorial O(N) model with a generic nearest-neighbor interaction W(\bsigma_i\cdot \bsigma_j) (depending on {\cal N} tunable parameters), a Yukawa (and Gross Neveu) model with N_f fermions at finite temperature and the…

This paper investigates the long-term dynamics of a reaction-diffusion predator-prey system subject to random environmental fluctuations modeled by Markovian switching. The model is formulated as a hybrid system of partial differential…