Generalized projection dynamics in evolutionary game theory

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function both locally and globally. By global (local) ray projection we mean a projection of the vector (close to the unit simplex) unto the unit simplex along a ray through the origin. For these dynamics, we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point, and that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium.
Then, we employ these projections on a set of functions related to the relative fitness function which yields a class containing e.g., best-response, logit, replicator, and Brown-Von-Neumann dynamics.