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

The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…

We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…

The convergence to equilibrium of renormalized solutions to reaction-cross-diffusion systems in a bounded domain under no-flux boundary conditions is studied. The reactions model complex balanced chemical reaction networks coming from…

A diffusion-limited annihilation process, A+B->0, with species initially separated in space is investigated. A heuristic argument suggests the form of the reaction rate in dimensions less or equal to the upper critical dimension $d_c=2$.…

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…

The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort…

In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We…

The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the…

Endangered populations often experience limited growth ability at low densities, a phenomenon described by the Allee effect. In this thesis, we investigate a predator-prey model incorporating the Allee effect within a two-dimensional…

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and…

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the…

We consider a one-dimensional, weakly asymmetric, boundary driven exclusion process on the interval $[0,N]\cap Z$ in the super-diffusive time scale $N^2 \epsilon^{-1}_N$, where $1\ll \epsilon^{-1}_N \ll N^{1/4}$. We assume that the external…

We analyze the propagation of excitons in a $d$-dimensional lattice with power-law hopping $\propto 1/r^\alpha$ in the presence of dephasing, described by a generalized Haken-Strobl-Reineker model. We show that in the strong dephasing…

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. We consider general dynamical exponent $z$, where $x_t\sim t^{1/z}$ is the rms diffusion distance after time $t$. At short…

This paper is devoted to a nonlocal reaction-diffusion-advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamic…

We investigate spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the…

This paper is concerned with the two-species chemotaxis-competition model with degenerate diffusion, \[\begin{cases} u_t = \Delta u^{m_1} - \chi_1 \nabla\cdot(u\nabla w) + \mu_1 u (1-u-a_1v), &x\in\Omega,\ t>0,\\% v_t = \Delta v^{m_2} -…

The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…

This is a continuation of our work \cite{dns-part1} to investigate the long-time dynamics of a two species competition model of Lotka-Volterra type with nonlocal diffusions, where the territory (represented by the real line $\R$) of a…