Imperial College London

ProfessorPierreDegond

Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 1474p.degond Website CV

 
 
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Location

 

6M38Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Degond,
author = {Degond, P and Engel, M and Liu, J-G and Pego, R},
journal = {Communications in Mathematical Sciences},
title = {A Markov jump process modelling animal group size statistics},
url = {http://hdl.handle.net/10044/1/73253},
}

RIS format (EndNote, RefMan)

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
SN - 1539-6746
TI - A Markov jump process modelling animal group size statistics
T2 - Communications in Mathematical Sciences
UR - http://hdl.handle.net/10044/1/73253
ER -