Format:
187 Seiten
,
Diagramme
Content:
In this thesis, stochastic dynamics modelling collective motions of populations, one of the most mysterious type of biological phenomena, are considered. For a system of N particle-like individuals, two kinds of asymptotic behaviours are studied : ergodicity and flocking properties, in long time, and propagation of chaos, when the number N of agents goes to infinity. Cucker and Smale, deterministic, mean-field kinetic model for a population without a hierarchical structure is the starting point of our journey : the first two chapters are dedicated to the understanding of various stochastic dynamics it inspires, with random noise added in different ways. The third chapter, an attempt to improve those results, is built upon the cluster expansion method, a technique from statistical mechanics. Exponential ergodicity is obtained for a class of non-Markovian process with non-regular drift. In the final part, the focus shifts onto a stochastic system of interacting particles derived from Keller and Segel 2-D parabolicelliptic model for ...
Note:
Dissertation Universität Potsdam 2017
,
Dissertation Université de Toulouse 2017
Additional Edition:
Erscheint auch als Online-Ausgabe Pédèches, Laure Stochastic models for collective motions of populations Potsdam, 2017
Language:
English
Keywords:
Stochastisches Modell
;
Schwarmverhalten
;
Hochschulschrift
Bookmarklink