The Existence Of Center And The For 3-dimensional Replicator Systems

Based on the sufficient and necessary conditions for the existence of center and the global stability of a feasible equilibrium in a two species Lotka-Volterra system, and by the equivalent reversible mapping between a two species Lotka-Volterra system and 3-dimensional replicator system, the sufficient and necessary conditions for the existence of center and the global stability of a feasible equilibrium in a 3-dimensional replicator system are obtained. Through the use of these conditions, we verify some known results and obtain some new ones.