Dynamic Behavior Of Cyclic Advantage System In Donation Game With Mutation

According to the necessary and sufficient conditions for the existence of the center and the global stability of the positive equilibrium in a three-dimensional replication system,a complete classification of the three-strategy cyclic dominance system of the donation game is obtained.By introducing mutation into the donation game,the existence of a small-amplitude limit cycle and a center of the three-dimensional replicator-catastrophe dynamic system is judged.The Permanence for the four-strategy cyclic dominance system is discussed.