Related papers: Coexistence for a multitype contact process with s…
We study the interface of the multitype contact process on $\mathbb{Z}$. In this process, each site of $\mathbb{Z}$ is either empty or occupied by an individual of one of two species. Each individual dies with rate 1 and attempts to give…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model…
We discuss general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Real-world examples of periods of periodical organisms range from cicadas whose life-cycles are larger prime numbers, like 13 or 17, to bamboos whose periods are large multiples of small primes, like 40 or even 120. The periodicity is…
A square lattice is introduced into the Penna model for biological aging in order to study the evolution of diploid sexual populations under certain conditions when one single locus in the individual's genome is considered as identifier of…
Interacting particle systems are continuous time Markov processes which are used to construct models in many disciplines. Monotonicity is a property that some interacting particle systems possess. A monotone interacting particle system is…
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…
This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the…
Reaction-diffusion systems with a Lotka-Volterra-type reaction term, also known as competition-diffusion systems, have been used to investigate the dynamics of the competition among $m$ ecological species for a limited resource necessary to…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes…
We introduce spatially explicit stochastic processes to model multispecies host-symbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence…
Camouflage in nature seems to arise from competition between predator and prey. To survive, predators must find prey, and prey must avoid being found. This work simulates an abstract model of that adversarial relationship. It looks at…
There are two types of particles interacting on a homogeneous tree of degree d + 1. The particles of the first type colonize the empty space with exponential rate 1, but cannot take over the vertices that are occupied by the second type.…
We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations. In addition to the usual contact repulsive interactions between the particles, the Hamiltonian has an…