Related papers: Free boundary problems for the diffusive competiti…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…
This paper explains the uniqueness of positive steady state of general Lotka-Volterra competition model of two species of animals in the same environment.
This paper studies the traveling wave solutions to a three species competition cooperation system. The existence of the traveling waves is investigated via monotone iteration method. The upper and lower solutions come from either the waves…
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and…
This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite…
The Lotka-Volterra system is a set of ordinary differential equations describing growth of interacting ecological species. This model has gained renewed interest in the context of random interaction networks. One of the debated questions is…
This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge…
We introduce and analyze a nonlocal version of the one-phase Stefan problem in which, as in the classical model, the rate of growth of the volume of the liquid phase is proportional to the rate at which energy is lost through the…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
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…
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…
We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearity and with free boundaries. These systems are used as multi-species competitive model. For two-species models, we prove the existence of a…
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 $i = i,\dots, k$, $s\in(0,1)$,…
The current paper is to investigate the numerical approximation of logistic type chemotaxis models in one space dimension with a free boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
In this paper, we investigate the uniform regularity and asymptotic behavior of solutions to the following Lotka-Volterra type system of strong competition with Dirichlet boundary conditions: \begin{align*} \left\{ \begin{array}{ll} -\Delta…
The current paper is concerned with the existence of spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in time and space periodic habitats. The notion of spreading speed intervals for such a…
We consider the reaction-diffusion competition system in the so-called {\it critical competition case}. The associated ODE system then admits infinitely many equilibria, which makes the analysis intricate. We first prove the non-existence…
In this thesis we use dynamical systems to analize the consequences of competition in the arrival of a foreign species in an ecosystem.
We introduce and study a class of free boundary models with "nonlocal diffusion", which are natural extensions of the free boundary models in Du and Lin [17] and elsewhere, where "local diffusion" is used to describe the population…