A multi-class extension of the mean field Bolker-Pacala population model
Probability
2016-11-01 v1
Abstract
We extend our earlier mean field approximation of the Bolker-Pacala model of population dynamics by dividing the population into N classes, using a mean field approximation for each class but also allowing migration between classes as well as possibly suppressive influence of the population of one class over another class. For N at least 2, we obtain one symmetric non-trivial equilibrium for the system and give global limit theorems. For N=2, we calculate all equilibrium solutions, which, under additional conditions, include multiple non-trivial equilibria. Lastly, we prove geometric ergodicity regardless of the number of classes when there is no population suppression across the classes.
Keywords
Cite
@article{arxiv.1610.09569,
title = {A multi-class extension of the mean field Bolker-Pacala population model},
author = {Mariya Bessonov and Stanislav Molchanov and Joseph Whitmeyer},
journal= {arXiv preprint arXiv:1610.09569},
year = {2016}
}