相关论文: Global dynamics of a general competition diffusion…
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…
We introduce and analyze a spatial Lotka-Volterra competition model with local and nonlocal interactions. We study two alternative classes of nonlocal competition that differ in how each species' characteristics determine the range of the…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
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…
Cyclic, nonhierarchical interactions among biological species represent a general mechanism by which ecosystems are able to maintain high levels of biodiversity. However, species coexistence is often possible only in spatially extended…
In this paper, we are concerned with a two-species competitive model with diffusive terms on a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The Lagrangian transformation…
This paper is concerned with a diffusive Lotka-Volterra cooperative modelwith population flux by attractive transition. We study the time-global well-posedness and the large time behavior of solutions in a case where the habitat is a…
We are interested in the long time behavior of a two-type density-dependent biological population conditioned to non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
In order to understand how impulsive interventions and environmental perturbations affect dynamics of competitors, we focus on a diffusive competition model with free boundaries and periodic pulses in a temporally heterogeneous environment…
In this article, we investigate a competitive reaction-diffusion system modelling the interaction between several species of mosquitoes. In particular, it has been observed that in tropical regions, Aedes aegypti mosquitoes are well…
This paper is concerned with the asymptotic spreading behavior of solutions of the Lotka-Volterra system with strong competition in $\mathbb{R}^{N}$. Two types of initial conditions are proposed: (C1) two species initially occupy bounded…
We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem $$(-\Delta)^s u_i = f_i(x,u_i) - \beta u_i^p \sum_{j\neq i} a_{ij} u_j^p,$$ where $i = i,\dots, k$, $s\in(0,1)$,…
Competition between species and genotypes is a dominant factor in a variety of ecological and evolutionary processes. Biological dynamics are typically highly stochastic, and therefore, analyzing a competitive system requires accounting for…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The…