{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T15:09:28Z","timestamp":1777475368482,"version":"3.51.4"},"reference-count":66,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2016,9,9]],"date-time":"2016-09-09T00:00:00Z","timestamp":1473379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/P505593\/1"],"award-info":[{"award-number":["EP\/P505593\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Games"],"abstract":"<jats:p>We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, and pair-exchange of neighboring individuals. Here, we study the influence of mobility on the emerging patterns and investigate when the pair-exchange rate is responsible for spiral waves to become elusive in stochastic lattice simulations. In particular, we show that the spiral waves predicted by the system\u2019s deterministic partial equations are found in lattice simulations only within a finite range of the mobility rate. We also report that in the absence of mutations and dominance-replacement, the resulting spiraling patterns are subject to convective instability and far-field breakup at low mobility rate. Possible applications of these resolution and far-field breakup phenomena are discussed.<\/jats:p>","DOI":"10.3390\/g7030024","type":"journal-article","created":{"date-parts":[[2016,9,9]],"date-time":"2016-09-09T10:36:06Z","timestamp":1473417366000},"page":"24","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games"],"prefix":"10.3390","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1424-567X","authenticated-orcid":false,"given":"Mauro","family":"Mobilia","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alastair","family":"Rucklidge","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bartosz","family":"Szczesny","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1126\/science.309.5731.90","article-title":"What Determines Species Diversity?","volume":"309","author":"Pennisi","year":"2005","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hofbauer, J., and Sigmund, K. 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