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dc.contributorVirginia Tech
dc.contributor.authorDurney, C. H.
dc.contributor.authorCase, S. O.
dc.contributor.authorPleimling, M.
dc.contributor.authorZia, R. K. P.
dc.date.accessioned2014-01-17T13:41:32Z
dc.date.available2014-01-17T13:41:32Z
dc.date.issued2011-05-09
dc.identifier.citationDurney, C. H. ; Case, S. O. ; Pleimling, M. ; et al., May 9, 2011. "Saddles, arrows, and spirals: Deterministic trajectories in cyclic competition of four species," PHYSICAL REVIEW E 83(5) Part 1: 051108. DOI: 10.1103/PhysRevE.83.051108
dc.identifier.issn1539-3755
dc.identifier.urihttp://hdl.handle.net/10919/24877
dc.description.abstractPopulation dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in configuration space of the population fractions. We discover a variety of orbits, shaped like saddles, spirals, and straight lines. Many of their properties are found explicitly. Most remarkably, we identify a collective variable that evolves simply as an exponential: Q proportional to e(lambda t), where lambda is a function of the reaction rates. It provides information on the state of the system for late times (as well as for t -> -infinity). We discuss implications of these results for the evolution of a finite, stochastic system. A generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems.
dc.description.sponsorshipUS National Science Foundation_DMR-0705152, DMR-0904999, DMR-1005417
dc.language.isoen_US
dc.publisherAmerican Physical Society
dc.subjectlotka-volterra systems
dc.subjectrock-paper-scissors
dc.subjectnon-linear transformations
dc.subject1st integrals
dc.subjectparity law
dc.subjectdynamics
dc.subjectmodel
dc.subjectgame
dc.subjectbiodiversity
dc.subjectpromotes
dc.subjectPhysics
dc.titleSaddles, arrows, and spirals: Deterministic trajectories in cyclic competition of four species
dc.typeArticle
dc.identifier.urlhttp://link.aps.org/doi/10.1103/PhysRevE.83.051108
dc.date.accessed2013-12-17
dc.title.serialPhysical Review E
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.83.051108


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