Feedback Controlled Bifurcation of Evolutionary Dynamics with Generalized Fitness

Biswadip Dey, Alessio Franci, Kayhan Ozcimder, Naomi Ehrich Leonard

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Coexistence and interaction of multiple strategies in a large population of individuals can be observed in a variety of natural and engineered settings. In this context, replicator-mutator dynamics provide an efficient tool to model and analyze the evolution of the fractions of the total population committed to different strategies. Although the literature addresses existence and stability of equilibrium points and limit cycles of these dynamics, linearity in fitness functions has typically been assumed. We generalize these dynamics by introducing a nonlinear fitness function, and we show that the replicator-mutator dynamics for two competing strategies exhibit a quintic pitchfork bifurcation. Then, by designing slow-time-scale feedback dynamics to control the bifurcation parameter (mutation rate), we show that the closed-loop dynamics can exhibit oscillations in the evolution of population fractions. Finally, we introduce an ultraslow-time-scale dynamics to control the associated unfolding parameter (asymmetry in the payoff structure), and demonstrate an even richer class of behaviors.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6049-6054
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
CountryUnited States
CityMilwauke
Period6/27/186/29/18

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Keywords

  • Bifurcation
  • Evolutionary Dynamics
  • Nonlinear Systems

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    Dey, B., Franci, A., Ozcimder, K., & Leonard, N. E. (2018). Feedback Controlled Bifurcation of Evolutionary Dynamics with Generalized Fitness. In 2018 Annual American Control Conference, ACC 2018 (pp. 6049-6054). [8431851] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431851