Emergence of periodic behaviours from randomness

[摘要] 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.

[发布机构] School of Mathematical Sciences, University of Nottingham, Nottingham; NG7 2RD, United Kingdom^1

[效力级别] 数学

[关键词] Adjacent nodes;Birth-death process;Closed loops;Discrete systems;Non-interacting particles;Relative value;Spatial structure;Underlying dynamics