相关论文: Minimal coexistence configurations for multispecie…

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 $i = i,\dots, k$, $s\in(0,1)$,…

In this paper we focus on existence and symmetry properties of solutions to the cubic Schr\"odinger system \[ -\Delta u_i +\lambda_i u_i = \sum_{j=1}^d \beta_{ij} u_j^2 u_i \quad \text{in $\Omega \subset \mathbb{R}^N$},\qquad i=1,\dots d \]…

The subject of this paper is inspired by \cite{CC} and \cite{CCP}. In \cite{CC} the authors investigate the dynamics of a population in a heterogeneous environment by means of diffusive logistic equations. An important part of their study…

We investigate the properties of nonlinear excitations in different types of soliton bearing systems with long-range dispersive interaction. We show that length-scale competition in such systems universally results in a multi-component…

We investigate spatially inhomogeneous versions of the stochastic Lotka-Volterra model for predator-prey competition and coexistence by means of Monte Carlo simulations on a two-dimensional lattice with periodic boundary conditions. To…

We consider the classical two-species Lotka-Volterra competition-diffusion system in the strong-weak competition case. When the corresponding minimal speed of the traveling waves is not linear determined, we establish the precise asymptotic…

In recent years there has been a growing interest in the study of the dynamics of stochastic populations. A key question in population biology is to understand the conditions under which populations coexist or go extinct. Theoretical and…

Recent work draws attention to community-community encounters ("coalescence") as likely an important factor shaping natural ecosystems. This work builds on MacArthur's classic model of competitive coexistence to investigate such…

Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…

Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…

We consider an ecological system governed by Lotka-Volterra dynamics and an example of an economic system as a mesomarket with perfect competition. We propose a mechanism for cooperative self-regulation that enables the system under…

We use dynamical generating functionals to study the stability and size of communities evolving in Lotka-Volterra systems with random interaction coefficients. The size of the eco-system is not set from the beginning. Instead, we start from…

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. Here we present a theory that integrates both aspects of mutant fitness by coupling the…

We introduce a minimal evolutionary model to show how local cooperation and global competition can create a transition to the diversity of communities such as linguistic groups. By using a lattice model with high-dimensional state agents…

This paper investigates the competition of two species in a heterogeneous environment subject to the effect of harvesting. The most realistic harvesting case is connected with the intrinsic growth rate, and the harvesting functions are…

The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance…

We show that spatial extensions of many-species population dynamics models, such as the Lotka-Volterra model with random interactions we focus on in this work, generically exhibit scale-free correlation functions of population sizes in the…

We study a generalized system of ODE's modeling a finite number of biological populations in a competitive interaction. We adapt the techniques in two previous articles to prove the convergence to a unique stable equilibrium.

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the…

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice and we give…