ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Alternate Models of Replicator Dynamics

Journal of Applied Nonlinear Dynamics 2(2) (2013) 193--206 | DOI:10.5890/JAND.2013.04.007

Elizabeth N. Wesson$^{1}$; Richard H. Rand$^{2}$

$^{1}$ Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA

$^{2}$ Department of Mathematics, Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA

Abstract

Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by ˙ xi = xi ( fi (x)−φ ) , i = 1, . . . ,n, where xi is the frequency of strategy i, fi is its fitness, and φ = Σn i=1 xi fi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A by taking fi(x) = (A · x)i. This model is based on the exponential model of population growth, ˙ xi = xi fi, with φ introduced in order both to hold the total population constant and to model competition between strategies. We analyze the dynamics of analogous models for the replicator equation of the form ˙ xi = g(xi)( fi −φ ), for selected growth functions g.

Acknowledgments

Thanks to David Rand for his helpful ideas and intuition when we were beginning work on this project.

References

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