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@article{Degond:2020:10.4310/CMS.2020.v18.n1.a3,
author = {Degond, P and Engel, M and Liu, J-G and Pego, R},
doi = {10.4310/CMS.2020.v18.n1.a3},
journal = {Communications in Mathematical Sciences},
pages = {55--89},
title = {A Markov jump process modelling animal group size statistics},
url = {http://dx.doi.org/10.4310/CMS.2020.v18.n1.a3},
volume = {18},
year = {2020}
}

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TY  - JOUR
AB  - We translate a coagulation-framentation model, describing the dynamics of animal group size distributions, into a model for the population distribution and associate the nonlinear evolution equation witha Markov jump process of a type introduced in classic work of H. McKean. In particular this formalizesa model suggested by H.-S. Niwa [J. Theo. Biol. 224 (2003)] with simple coagulation and fragmentationrates. Based on the jump process, we develop a numerical scheme that allows us to approximate the equilibrium for the Niwa model, validated by comparison to analytical results by Degond et al. [J. NonlinearSci. 27 (2017)], and study the population and size distributions for more complicated rates. Furthermore,the simulations are used to describe statistical properties of the underlying jump process. We additionally discuss the relation of the jump process to models expressed in stochastic differential equations anddemonstrate that such a connection is justified in the case of nearest-neighbour interactions, as opposedto global interactions as in the Niwa model.
AU  - Degond,P
AU  - Engel,M
AU  - Liu,J-G
AU  - Pego,R
DO  - 10.4310/CMS.2020.v18.n1.a3
EP  - 89
PY  - 2020///
SN  - 1539-6746
SP  - 55
TI  - A Markov jump process modelling animal group size statistics
T2  - Communications in Mathematical Sciences
UR  - http://dx.doi.org/10.4310/CMS.2020.v18.n1.a3
UR  - http://hdl.handle.net/10044/1/73253
VL  - 18
ER  -

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