  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.
