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Effect of interaction strength on the evolution of cooperation

Cooperative behaviors are ubiquitous in nature,which is a puzzle to evolutionary biology,because the defector always gains more benefit than the cooperator,thus,the cooperator should decrease and vanish over time.This typical "prisoners' dilemma" phenomenon has been widely researched in recent years.The interaction strength between cooperators and defectors is introduced in this paper(in human society,it can be understood as the tolerance of cooperators).We find that only when the maximum interaction strength is between two critical values,the cooperator and defector can coexist,otherwise, 1) if it is greater than the upper value,the cooperator will vanish, 2) if it is less than the lower value,a bistable state will appear.