A Markov jump process modelling animal group size statistics
| Autor: | Robert L. Pego, Maximilian Engel, Jian-Guo Liu, Pierre Degond |
|---|---|
| Přispěvatelé: | Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), department of mathematics, University of Maryland [College Park], University of Maryland System-University of Maryland System, Center for Nonlinear Analysis [Pittsburgh] (CNA), Carnegie Mellon University [Pittsburgh] (CMU), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), The Royal Society, Engineering & Physical Science Research Council (EPSRC) |
| Rok vydání: | 2020 |
| Předmět: |
POPULATION BALANCE-EQUATIONS
DYNAMICS Work (thermodynamics) Population dynamics q-bio.PE General Mathematics Population Mathematics Applied self-consistent Markov process COAGULATION jump process 01 natural sciences 0101 Pure Mathematics 010104 statistics & probability Stochastic differential equation 92D50 Simple (abstract algebra) 0102 Applied Mathematics CONVERGENCE DISTRIBUTIONS 65C30 Statistical physics [MATH]Mathematics [math] 0101 mathematics Quantitative Biology - Populations and Evolution education 65C35 Mathematics 45J05 education.field_of_study Science & Technology fish schools SCHEME Applied Mathematics 010102 general mathematics Populations and Evolution (q-bio.PE) 1502 Banking Finance and Investment 70F45 AGGREGATION self-consistent Markov process Mathematics Subject Classification (2010): 60J75 Connection (mathematics) Nonlinear system Distribution (mathematics) FOS: Biological sciences Physical Sciences Jump process numerics |
| Zdroj: | Communications in Mathematical Sciences Communications in Mathematical Sciences, International Press, 2020, 18, pp.55-89 Communications in Mathematical Sciences, 2020, 18, pp.55-89 |
| ISSN: | 1945-0796 1539-6746 |
| DOI: | 10.4310/cms.2020.v18.n1.a3 |
| Popis: | International audience; 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 with a Markov jump process of a type introduced in classic work of H. McKean. In particular this formalizes a model suggested by H.-S. Niwa [J. Theo. Biol. 224 (2003)] with simple coagulation and fragmentation rates. 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. Nonlinear Sci. 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 and demonstrate that such a connection is justified in the case of nearest-neighbour interactions, as opposed to global interactions as in the Niwa model. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|