Completely Algebraic Classification For 3-Dimensional Replicator Systems With A Positive Equilibrium

Based on the classification conditions for a two species Lotka-Volterra system with a positive equilibrium,and the homeomorphism mapping between a two species Lotka-Volterra system and a three-dimensional replicator system,the completely algebraic classifica-tion of dynamical behaviors and their corresponding phase diagrams are obtained.Through the use of these conditions,we verify some known results and obtain some new ones.