title: Phase transitions in multiplicative competitive processes.
abstract: We introduce a discrete multiplicative process as a generic model of competition. Players with different abilities successively join the game and compete for finite resources. Emergence of dominant players and evolutionary development occur as a phase transition. The competitive dynamics underlying this transition is understood from a formal analogy to statistical mechanics. The theory is applicable to bacterial competition, predicting novel population dynamics near criticality.
authors.affiliation: Department of Physics, Graduate School of Science, Kyoto University, Japan.
authors.forename: Hideaki
authors.initials: H
authors.lastname: Shimazaki
authors.forename: Ernst
authors.initials: E
authors.lastname: Niebur
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior; D017753:Ecosystem; D005716:Game Theory; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009154:Mutation; D011157:Population Dynamics; D012919:Social Behavior; D013269:Stochastic Processes; D013696:Temperature; D013997:Time Factors