Phase transition and 1/fnoise in a game dynamical model

We study a population of interacting species, described by the replicator model well established in theoretical biology. Using methods of statistical physics we present an exact steady-state solution to the model as a function of the population's cooperation pressure u when the number of species is large and the interactions are taken as random. When u is lowered to a critical value ${\mathit{u}}_{\mathit{c}}$, the solution becomes unstable. This phase transition manifests itself by a 1/f behavior in the power spectrum of the system's response against weak external noise.