arXiv subjects

Christian H. S. Hamster

Publications and source records attributed to Christian H. S. Hamster.

2 recordsLinked to original sources

arXiv2025

Conditional Speed and Shape Corrections for Travelling Wave Solutions to Stochastically Perturbed Reaction-Diffusion Systems

In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a stochastic freezing approach that allows effective limiting information to be extracted concerning the behaviour of the stochastic perturbations from the deterministic wave. As an application, this allows us to provide a rigorous definition for the stochastic corrections to the wave speed. In addition, our approach allows their size to be computed to any desired order in the noise strength, provided that sufficient smoothness is available.

math.AP↗

arXiv2022

Speciation in a MacArthur model predicts growth, stability and adaptation in ecosystems dynamics

Ecosystems dynamics is often considered as driven by a coupling of species' resource consumption and its population size dynamics. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature that would also need to be captured by such models is the introduction of new and different species. Speciation introduces a stochastic component in the otherwise deterministic MacArthur theory. We describe here how speciation can be implemented to yield a model that is consistent with current theory on equilibrium resource-consumer models, but also displays readily observable rank diversity metric changes. The model also reproduces a priority effect. Adding speciation to a MacArthur-style model so provides an attractively simple extension to explore the rich dynamics in evolving ecosystems.

q-bio.PE↗