@article { , 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.}, doi = {10.1038/s41598-016-0022-3}, eissn = {2045-2322}, issue = {21}, journal = {Scientific Reports}, publicationstatus = {Published}, publisher = {Nature Publishing Group}, url = {https://nottingham-repository.worktribe.com/output/832458}, volume = {6}, author = {Pickton, John and Hopcraft, Keith Iain and Jakeman, Eric} }