Universal properties of population dynamics with fluctuating resources
Statistical Mechanics
2009-11-13 v1
Abstract
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (Model A) dynamics. Two new operators emerge, with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point, suggesting a crossover to a first order transition from the active (surviving) to the inactive (extinct) state.
Cite
@article{arxiv.0706.0450,
title = {Universal properties of population dynamics with fluctuating resources},
author = {Sayak Mukherjee and H. K. Janssen and B. Schmittmann},
journal= {arXiv preprint arXiv:0706.0450},
year = {2009}
}