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Spatial many-species predator-prey systems have been shown to yield very rich space-time patterns. This observation begs the question whether there exist universal mechanisms for generating this type of emerging complex patterns in…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
In large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple…
We study a spatial cyclic predator-prey model with an even number of species (for n=4, 6, and 8) that allows the formation of two defective alliances consisting of the even and odd label species. The species are distributed on the sites of…
This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…
Competing strategies in an evolutionary game model, or species in a biosystem, can easily form a larger unit which protects them from the invasion of an external actor. Such a defensive alliance may have two, three, four or even more…
Interactions among multiple infectious agents are increasingly recognized as a fundamental issue in the understanding of key questions in public health, regarding pathogen emergence, maintenance, and evolution. The full description of…
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial,…
We study a class of elliptic competition-diffusion systems of long range segregation models for two and more competing species. The existence and uniqueness of the solution are shown. We prove that as the competition rate goes to infinity…
We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space…
We study a set of six-species ecological models where each species has two predators and two preys. On a square lattice the time evolution is governed by iterated invasions between the neighboring predator-prey pairs chosen at random and by…
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…
The self-protection of alliances against external invaders is a key concept behind the maintenance of biodiversity in the face of natural selection. But since these alliances, which can be formed by different numbers of competitors, can…
A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…
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…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
How large ecosystems can create and maintain the remarkable biodiversity we see in nature is probably one of the biggest open questions in science, attracting attention from different fields, from Theoretical Ecology to Mathematics and…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…