Saddles, arrows, and spirals: Deterministic trajectories in cyclic competition of four species

Simple item page
dc.contributorVirginia Techen
dc.contributor.authorDurney, C. H.en
dc.contributor.authorCase, S. O.en
dc.contributor.authorPleimling, Michel J.en
dc.contributor.authorZia, Royce K. P.en
dc.contributor.departmentPhysicsen
dc.date.accessed2013-12-17en
dc.date.accessioned2014-01-17T13:41:32Zen
dc.date.available2014-01-17T13:41:32Zen
dc.date.issued2011-05-09en
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.en
dc.description.sponsorshipUS National Science Foundation_DMR-0705152, DMR-0904999, DMR-1005417en
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.83.051108en
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.83.051108en
dc.identifier.issn1539-3755en
dc.identifier.urihttp://hdl.handle.net/10919/24877en
dc.identifier.urlhttp://link.aps.org/doi/10.1103/PhysRevE.83.051108en
dc.language.isoen_USen
dc.publisherAmerican Physical Societyen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectlotka-volterra systemsen
dc.subjectrock-paper-scissorsen
dc.subjectnon-linear transformationsen
dc.subject1st integralsen
dc.subjectparity lawen
dc.subjectdynamicsen
dc.subjectmodelen
dc.subjectgameen
dc.subjectbiodiversityen
dc.subjectpromotesen
dc.subjectPhysicsen
dc.titleSaddles, arrows, and spirals: Deterministic trajectories in cyclic competition of four speciesen
dc.title.serialPhysical Review Een
dc.typeArticle - Refereeden

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
PhysRevE.83.051108.pdf
Size:
888.67 KB
Format:
Adobe Portable Document Format
Description:
Main article
Download

Collections

Scholarly Works, Physics