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We consider a contact process on $Z^d$ with two species that interact in a symbiotic manner. Each site can either be vacant or occupied by individuals of species $A$ and/or $B$. Multiple occupancy by the same species at a single site is…

Probability · Mathematics 2019-12-11 Rick Durrett , Dong Yao

We study a generalization of the two colors multitype contact process intended to mimic an example of interspecific competition called allelopathy.

Probability · Mathematics 2007-05-23 Nicolas Lanchier

Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. This work, together with two…

Chaotic Dynamics · Physics 2007-05-23 Ricardo Lopez-Ruiz , Daniele Fournier-Prunaret

In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…

Analysis of PDEs · Mathematics 2024-08-07 Pablo Álvarez-Caudevilla , Cristina Brändle , Mónica Molina-Becerra , Antonio Suárez

We consider a symmetric finite-range contact process on $\mathbb{Z}$ with two types of particles (or infections), which propagate according to the same supercritical rate and die (or heal) at rate $1$. Particles of type 1 can occupy any…

Probability · Mathematics 2019-07-31 Mariela Pentón Machado

Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host--parasitoid model. In the case of…

Populations and Evolution · Quantitative Biology 2009-01-16 Matti Peltomaki , Martin Rost , Mikko Alava

This paper is devoted to the analysis of a reaction-diffusion system with strong competition and spatial heterogeneities modelling the interaction between two species of mosquitoes. In particular, we propose a mathematical model that…

Analysis of PDEs · Mathematics 2025-06-19 Nicolas Vauchelet

Motivated by a model of an area-wide integrated pest management, we develop an interacting particle system evolving in a random environment. It is a generalised contact process in which the birth rate takes two possible values, determined…

Probability · Mathematics 2015-08-27 Kevin Kuoch

The contact process on an infinite homogeneous tree is shown to exhibit at least two phase transitions as the infection parameter lambda is varied. For small values of lambda a single infection eventually dies out. For larger lambda the…

Probability · Mathematics 2007-05-23 Robin Pemantle

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…

Populations and Evolution · Quantitative Biology 2008-08-26 G. Szabo , A. Szolnoki , I. Borsos

We consider a class of multi-type particle systems having similar structure to the contact process and show that additivity is equivalent to the existence of a dual process, extending a result of Harris. We give two additional…

Probability · Mathematics 2014-10-20 Eric Foxall

Models relating to the Species-Area curve are usually defined at the species level, and concerned only with ecological timescales. We examine an individual-based model of co-evolution on a spatial lattice based on the Tangled Nature model,…

Populations and Evolution · Quantitative Biology 2007-05-23 Daniel Lawson , Henrik Jeldtoft Jensen

We consider a two-type contact process on $\Z$ in which both types have equal finite range and supercritical infection rate. We show that a given type becomes extinct with probability 1 if and only if, in the initial configuration, it is…

Probability · Mathematics 2010-04-13 Daniel Valesin

Interacting particle systems of interest in evolutionary game theory introduced in the probability literature consist of variants of the voter model in which each site is occupied by one player. The goal of this paper is to initiate the…

Probability · Mathematics 2024-12-31 Jonas Köppl , Nicolas Lanchier , Max Mercer

We propose the following model for speciation and extinction. Birth and deaths occur according to spatially inhomogeneous contact rates. We assume that the ratio of the birth rate over the death rate at a site converges to some limit as the…

Probability · Mathematics 2015-06-15 Rinaldo B. Schinazi

According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…

Populations and Evolution · Quantitative Biology 2017-08-16 Marcelo Martins de Oliveira , Ronald Dickman

Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail…

Physics and Society · Physics 2026-04-02 Juliette Gambaudo , Mathieu Génois

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…

Populations and Evolution · Quantitative Biology 2023-01-03 Violeta Calleja-Solanas , Nagi Khalil , Jesús Gómez-Gardeñes , Emilio Hernández-García , Sandro Meloni

In this paper, we introduce a type switching mechanism for the Contact Process on the lattice $\mathbb{Z}^d$. That is, we allow the individual particles/sites to switch between two (or more) types independently of one another, and the…

Probability · Mathematics 2024-07-02 Jochen Blath , Felix Hermann , Michel Reitmeier

When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or…

Physics and Society · Physics 2019-02-20 Kevin E. Bassler , Erwin Frey , R. K. P. Zia