We consider a population engaged in continuous public goods games. In our study, the lowest contributor in each game will be removed from the group, meanwhile new players will be added to the network to maintain the constant population size. Here, each new node would establish some connections with the existing ones in the network. We conclude that appropriate interaction numbers of each newcomer support the emergence and maintenance of cooperation for the continuous public goods game. Furthermore, the initial regular network has been driven to a slowly varying non-regular heterogeneous network which facilitates the evolution of cooperation. By investigating the resulting distribution of individual contributions, we show that provision of common goods can be fostered by permitting players target punishment on the lowest contributor in each continuous public goods game. We hope that our proposed model presents a feasible mechanism for promoting the emergence and evolution of cooperative behaviors.
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