Coexistence and duality in competing species models

2018/02/28 by Yu-Ting Chen, Chen, Yu-Ting, Matthias Hammer +1
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Social Sciences · #Complex Systems and Time Series Analysis #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1802.10476

openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss some stochastic spatial generalizations of the Lotka--Volterra model for competing species. The generalizations take the forms of spin systems on general discrete sets and interacting diffusions on integer lattices. Methods for proving coexistence in these generalizations and some related open questions are discussed. We use duality as the central point of view. It relates coexistence of the models to survival of their dual processes.

Related

• General Properties of a System of S Species Competing Pairwise
• Coexistence of Species in a Competition Model on Random Geometric Graphs
• Global behavior of N competing species with strong diffusion: diffusion leads to exclusion
• Interacting population models with pack behavior
• Stable trimorphic coexistence in a lattice model of spatial competition with two site types