Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics

Elizabeth Wesson () and Richard Rand
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Elizabeth Wesson: Cornell University
Richard Rand: Cornell University

Dynamic Games and Applications, 2016, vol. 6, issue 1, No 7, 139-156

Abstract: Abstract We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval $$T$$ T . Taking $$T$$ T as a bifurcation parameter, we demonstrate the existence of (non-degenerate) Hopf bifurcations in these systems and present an analysis of the resulting limit cycles using Lindstedt’s method.

Keywords: Replicator; Delay; Hopf bifurcation; Limit cycle; Lindstedt (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13235-015-0138-2

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