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We present a physical theory of buses serving a loop of bus stops as a ring of coupled self-oscillators, analogous to the Kuramoto model. Sustained bunching is a repercussion of the process of phase synchronisation whereby the phases of the oscillators are locked to each other. This emerges when demand exceeds a critical threshold. Buses also bunch at low demand, albeit temporarily, due to frequency detuning arising from different human drivers\u2019 distinct natural speeds. We calculate the critical transition when <jats:italic>complete phase locking<\/jats:italic> (full synchronisation) occurs for the bus system, and posit the critical transition to <jats:italic>completely no phase locking<\/jats:italic> (zero synchronisation). The intermediate regime is the phase where clusters of partially phase locked buses exist. Intriguingly, these theoretical results are in close correspondence to real buses in a university\u2019s shuttle bus system.<\/jats:p>","DOI":"10.1038\/s41598-019-43310-7","type":"journal-article","created":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T10:04:46Z","timestamp":1556877886000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Bus bunching as a synchronisation phenomenon"],"prefix":"10.1038","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3621-3799","authenticated-orcid":false,"given":"Vee-Liem","family":"Saw","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ning Ning","family":"Chung","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei Liang","family":"Quek","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi En Ian","family":"Pang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lock Yue","family":"Chew","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,5,3]]},"reference":[{"key":"43310_CR1","unstructured":"Pikovsky, A., Rosenblum, M. & Kurths, J. 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