Abstract
We study the long-time behavior of solutions to a measure-valued selection-mutation model that we formulated in [14]. We establish permanence results for the full model, and we study the limiting behavior even when there is more than one strategy of a given fitness; a case that arises in applications. We show that for the pure selection case the solution of the dynamical system converges to a Dirac measure centered at the fittest strategy class provided that the support of the initial measure contains a fittest strategy; thus we term this Dirac measure an Asymptotically Stable Strategy. We also show that when the strategy space is discrete, the selection-mutation model with small mutation has a locally asymptotically stable equilibrium that attracts all initial conditions that are positive at the fittest strategy.
Original language | English (US) |
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Pages (from-to) | 1472-1505 |
Number of pages | 34 |
Journal | Journal of Differential Equations |
Volume | 261 |
Issue number | 2 |
DOIs | |
State | Published - Jul 15 2016 |
Keywords
- Asymptotically stable strategy
- Cone of nonnegative measures
- Evolutionary game theory
- Lyapunov functions
- Persistence theory
- Survival of the fittest
ASJC Scopus subject areas
- Analysis
- Applied Mathematics