Some Combinatorial Aspects of Discrete Non-linear Population Dynamics
Chaotic Dynamics
2016-10-20 v1 Populations and Evolution
Abstract
Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.
Keywords
Cite
@article{arxiv.1610.05919,
title = {Some Combinatorial Aspects of Discrete Non-linear Population Dynamics},
author = {Nicolas Grosjean and Thierry Huillet},
journal= {arXiv preprint arXiv:1610.05919},
year = {2016}
}