Resident-invader dynamics in infinite dimensional systems

Research output: Contribution to journalArticle

Abstract

Motivated by evolutionary biology, we study general infinite-dimensional dynamical systems involving two species - the resident and the invader. Sufficient conditions for competition exclusion phenomena are given when the two species play similar, but distinct, strategies. Those conditions are based on invasibility criteria, for instance, evolutionarily stable strategies in the framework of adaptive dynamics.These types of questions were first proposed and studied by S. Geritz et al. and S. Geritz for a class of ordinary differential equations. We extend and generalize previous work in two directions. Firstly, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we devise an argument based on Hadamard's graph transform method that does not depend on the monotonicity of the two-species system. Our results are applicable to a wide class of reaction-diffusion models as well as models with nonlocal diffusion operators.

Original languageEnglish (US)
JournalJournal of Differential Equations
DOIs
StateAccepted/In press - Jun 25 2016

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Infinite-dimensional Systems
Ordinary differential equations
Nonlocal Diffusion
Evolutionarily Stable Strategy
Infinite Dimensional Dynamical System
Adaptive Dynamics
Semiflow
Dynamical systems
Reaction-diffusion Model
Infinite-dimensional Spaces
Biology
Monotonicity
Ordinary differential equation
Transform
Distinct
Generalise
Sufficient Conditions
Graph in graph theory
Operator
Class

ASJC Scopus subject areas

  • Analysis

Cite this

Resident-invader dynamics in infinite dimensional systems. / Cantrell, Robert; Cosner, George; Lam, King Yeung.

In: Journal of Differential Equations, 25.06.2016.

Research output: Contribution to journalArticle

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