Heteroclinic Chaos, Chaotic Itinerancy and Neutral Attractors in Symmetrical Replicator Equations with Mutations

抄録

A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: 1) the closer a system approaches a heteroclinic cycle, the exponentially longer a single species dominates a population and 2) there is coexistence of different heteroclinic cycles. A mutation introduces some new aspects: the emergence of structurally stable attractors and chaotic itinerant behavior. In addition, it is reported that a neutral attractor can exist in the μ → +0 region.