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Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's…

Wagner's modularity inducing problem domain is a key contribution to the study of the evolution of modularity, including both evolutionary theory and evolutionary computation. We study its behavior under classical genetic algorithms. Unlike…

Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved…

We study a class of geometric covering and packing problems for bounded regions on the plane. We are given a set of axis-parallel line segments that induces a planar subdivision with a set of bounded (rectilinear) faces. We are interested…

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

Competition for a limited resource is the hallmark of many complex systems, and often, that resource turns out to be the physical space itself. In this work, we study a novel model designed to elucidate the dynamics and emergence in complex…

A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…

Systems composed of distinct complex networks are present in many real-world environments, from society to ecological systems. In the present paper, we propose a network model obtained as a consequence of interactions between two species…

We study a four species ecological system with cyclic dominance whose individuals are distributed on a square lattice. Randomly chosen individuals migrate to one of the neighboring sites if it is empty or invade this site if occupied by…

A simple cellular automata model for a two-group war over the same territory is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are…

In this paper we consider a competition system in which two diseases spread by contact. We characterize the system behavior, establishing that only some configurations are possible. In particular we discover that coexistence of the two…

We investigate the evolution of competing languages, a subject where much previous literature suggests that the outcome is always the domination of one language over all the others. Since coexistence of languages is observed in reality, we…

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as…

A microscopic agent dynamical model for diploid age-structured populations is used to study evolution of polymorphism and sympatric speciation. The underlying ecology is represented by a unimodal distribution of resources of some width.…

We study an elementary problem of the topological robotics: collective motion of a set of $n$ distinct particles which one has to move from an initial configuration to a final configuration, with the requirement that no collisions occur in…

We introduce a spatially explicit model for the competition between type $a$ and type $b$ alleles. Each vertex of the $d$-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or…

In this paper, we provide new discrete uniformization theorems for bounded, $m$-connected planar domains. To this end, we consider a planar, bounded, $m$-connected domain $\Omega$ and let $\bord\Omega$ be its boundary. Let $\mathcal{T}$…

This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at…

Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with an affine mapping, and is therefore more complicated than…