Emergence of periodic behaviours from randomness

This paper discusses how periodic behaviours can arise in discrete systems where the underlying dynamics are purely random. We consider non-interacting particles moving randomly on a network of nodes forming a closed loop. The population dynamics describing the number of particles at a node is a sto...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. Conference series 2015-09, Vol.633 (1), p.12121
Main Authors: Pickton, J N, Hopcraft, K I, Jakeman, E
Format: Article
Language:English
Subjects:
Closed loops
Discrete systems
Markov processes
Nodes
Physics
Randomness
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper discusses how periodic behaviours can arise in discrete systems where the underlying dynamics are purely random. We consider non-interacting particles moving randomly on a network of nodes forming a closed loop. The population dynamics describing the number of particles at a node is a stochastic birth-death process, augmented by particles migrating randomly to adjacent nodes. This can result in the emergence of periodic behaviours occurring because of the interaction between the dynamics of the particles and the spatial structure through which they move. The conditions for this requires the network to comprise of three or more nodes and the migration to have a preferred direction. Moreover there are three classes of equilibria for the populations at nodes that depend on the relative values of the migration and birth rates.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/633/1/012121