相关论文: Dynamics of a Reaction-Diffusion Benthic-Drift Mod…
We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive $\alpha$-stable random measures. Such a SDE system can be identified as a…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
We consider a drift-diffusion model, with an unknown function depending on the spatial variable and an additional structural variable, the amount of ingested lipid. The diffusion coefficient depends on this additional variable. The drift…
The idea of a metapopulation has become canonical in ecology. Its original mean field form provides the important intuition that migration and extinction interact to determine the dynamics of a population composed of subpopulations. From…
We model the evolution of two competing populations $U_t, V_t $ by a two-dimensional size-dependent branching process. The population characteristics are assumed to be close to each other, as in a resident-mutant situation. Given that $U_t…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating…
We extend the $N$ branching Brownian motions model of population invasion to higher-order asexual reproduction. Increasing reproduction order leads to qualitative changes: invasion fronts generically cease to exist beyond binary…
Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes…
A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. However, many species are…
The basic model of purposeful kinesis was developed recently (Gorban and Cabukoglu, Ecol. Complex. 2018, 33, 75 83) on the basis of the let well enough alone idea. According to this model the diffusion drops while the reproduction…
Environmental fluctuations can create population-depleted areas and even extinct areas for the population. This effect is more severe in the presence of the Allee effect (decreasing growth rate at low population densities). Dispersal inside…
Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…
In ecology, species can mitigate their extinction risks in uncertain environments by diversifying individual phenotypes. This observation is quantified by the theory of bet-hedging, which provides a reason for the degree of phenotypic…
We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the…
This work is devoted to the study of a stochastic logistic growth model with and without the Allee effect. Such a model describes the evolution of a population under environmental stochastic fluctuations and is in the form of a stochastic…
We introduce a class of branching processes in which the reproduction or lifetime distribution at a given time depends on the total cumulative number of individuals who have been born in the population until that time. We focus on a…
We study large deviations asymptotics for a class of unbounded additive functionals, interpreted as normalized accumulated areas, of one-dimensional Langevin diffusions with sub-linear gradient drifts. Our results provide parametric…
In this paper, we study a two stream species Lotka-Volterra competition patch model with the patches aligned along a line. The two species are supposed to be identical except for the diffusion rates. For each species, the diffusion rates…
The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context…