title: The emergence of waves in random discrete systems.
abstract: Essential criteria for the emergence of wave-like manifestations occurring in an entirely discrete system are identified using a simple model for the movement of particles through a network. The dynamics are entirely stochastic and memoryless involving a birth-death-migration process. The requirements are that the network should have at least three nodes, that migration should have a directional bias, and that the particle dynamics have a non-local dependence. Well defined bifurcations mark transitions between amorphous, wave-like and collapsed states with an intermittent regime between the latter two.
authors.affiliation: University of Nottingham, School of Mathematical Sciences, Nottingham, NG7 2RD, UK. pmxjp5@nottingham.ac.uk.
authors.forename: John
authors.initials: J
authors.lastname: Pickton
authors.affiliation: University of Nottingham, School of Mathematical Sciences, Nottingham, NG7 2RD, UK.
authors.forename: Keith Iain
authors.initials: KI
authors.lastname: Hopcraft
authors.affiliation: University of Nottingham, School of Mathematical Sciences, Nottingham, NG7 2RD, UK.
authors.forename: Eric
authors.initials: E
authors.lastname: Jakeman