Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by
i = 1,…, n, where xi is the frequency, or relative abundance, of strategy i, fi is its fitness, and is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A, where Ai,j is the expected payoff of i vs. j, by taking fi(x) = (A·x)i. This model is based on the exponential model of population growth, ẋi = xifi, 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
for selected growth functions g.
Volume Subject Area:9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
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