Related papers: Coexistence and duality in competing species model…
We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing…
This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.
A fundamental problem in evolutionary ecology research is to explain how different species coexist in natural ecosystems. This question is directly related with species trophic competition. However, competition theory, based on the…
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to the necessary conditions. In addition, convergence in distribution of positive…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Dirichlet boundary conditions. For a class of nonconvex domains composed by balls connected with thin corridors, we show the occurrence of pattern…
The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes…
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…
Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
This paper is concerned with a nonlocal diffusion Lotka-Volterra type competition model that consisting of a native species and an invasive species in a one-dimensional habitat with free boundaries. We prove the well-posedness of the system…
In a diverse population, where many species are present, competitors can fight for surviving at individual and collective levels. In particular, species, which would beat each other individually, may form a specific alliance that ensures…
We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one…
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…
We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we…
We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows…
We investigate the global dynamics of a special case of the classical Lotka-Volterra competition-diffusion system in spatially heterogeneous environment. This model indicates that the evolution of the density of the predator is independent…
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The…
A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…