Emergence of periodic behaviours from randomness. (August 2015)

• Record Type: Journal Article
• Authors: Pickton, J N; Hopcraft, K I; Jakeman, E
• Is Part Of: Journal of physics. Number 633(2015)
• Publication Date: 2015-08
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/633/1/012121
• Languages: English
• ISSNs: 1742-6588

Abstract

Abstract: 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.