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Hopf Bifurcations in Two-Player Delayed Replicator Dynamics

[+] Author Affiliations
Elizabeth Wesson, Richard Rand

Cornell University, Ithaca, NY

Paper No. DETC2014-35404, pp. V008T11A055; 8 pages
doi:10.1115/DETC2014-35404
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 8: 26th Conference on Mechanical Vibration and Noise
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4641-4
  • Copyright © 2014 by ASME

abstract

We investigate the dynamics of two-strategy replicator equations in which competition between strategies is delayed by a given time interval T. Taking 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.

Copyright © 2014 by ASME

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