The stable classes and the codimension-one bifurcations of the planar replicator system

The nine-dimensional parameter space of the planar replicator system is reduced to a 3-torus and the stratified into 19 different components which are shown to be the stable classes of the system. A complete list of the 38 codimension-one bifurcations in the system is obtained and it is shown that the transversal deformations of topologically similar codimension-one flows with no cycle of saddles are equivalent.