Cooperator driven oscillation in a time-delayed feedback-evolving game

Considering feedback of collective actions cooperation on common resources has vital importance to reach sustainability. But such efforts may have not immediate consequence the state environment and it is unclear how they influence strategic environmental dynamics with feedbacks. To address this issue, we construct a feedback-evolving game model in which consider growth capacity punishment efficiency defectors who do provide returns environment. Importantly, further assume delay adopting contribution cooperative individuals change our model. We find that when amount from cooperators' endowment fixed, time no particular coevolutionary dynamics. However, return proportional their endowment, then can induce periodic oscillatory level Our work reveals potential effects interactions feedback.