Related papers: Some "counterintuitive" results in two species com…
We examine the two-dimensional extension of the model of Kessler and Sander of competition between two species identical except for dispersion rates. In this class of models, the spatial inhomogeneity of reproduction rates gives rise to an…
Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially,…
We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population,…
This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global…
In this paper, we study the dynamics of a two-species competition model with two different free boundaries in heterogeneous time-periodic environment, where the two species adopt a combination of random movement and advection upward or…
This paper mainly focuses on the sign of the wave speed in the Lotka-Volterra competition system of bistable type, also known as the strong-strong competition case. The traveling wave solution of the system is crucial for understanding the…
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable,…
We study the effect of speciation, i.e. the introduction of new species through evolution into communities, in the setting of predator-prey systems. Predator-prey dynamics is classically well modeled by Lotka-Volterra equations, also when…
The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied,…
We consider a population of agents competing for finite resources using strategies based on two channels of signals. The model is applicable to financial markets, ecosystems and computer networks. We find that the dynamics of the system is…
The Lotka--Volterra competition system with diffusion is considered. The Painlev\'e property of this system is investigated. Exact traveling wave solutions of the Lotka--Volterra competition system are found. Periodic solutions expressed in…
In this paper we investigate some free boundary problems for the Lotka-Volterra type prey-predator model in one space dimension. The main objective is to understand the asymptotic behavior of the two species (prey and predator) spreading…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
Seasonality frequently occurs in population models, and the corresponding seasonal patterns have been of great interest to scientists. This paper is concerned with traveling waves to a time-periodic bistable Lotka-Volterra competition…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
This work is devoted to prove uniqueness result for the positive solution to a strongly competing system of Lotka - Volterra type in the limiting configuration, when the competition rate tends to infinity.
In this paper, we investigate a two-species competition model in a landscape consisting of a finite number of adjacent patches. For the two-patch scenario, by treating edge behavior at the interface as a strategy, it has been shown that…
Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a…
We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the…
Arthur's (1988) model for competing technologies is discussed from the perspective of evolution theory. Using Arthur's own model for the simulation, we show that 'lock-ins' can be suppressed by adding reflexivity or uncertainty on the side…