Cooperative behaviors are ubiquitous in nature and human society.It is very important to understand the internal mechanism of emergence and maintenance of cooperation.As we know now,the offsprings inherit not only the phenotype but also the neighborhood relationship of their parents.Some recent research results show that the interactions among individuals facilitate survival of cooperation through network reciprocity of clustering cooperators.This paper aims at introducing an inheritance mechanism of neighborhood relationship to explore the evolution of cooperation.In detail,a mathematical model is proposed to characterize the evolutionary process with the above inheritance mechanism.Theoretical analysis and numerical simulations indicate that high-level cooperation can emerge and be maintained for a wide variety of cost-to-benefit ratios,even if mutation happens during the evolving process.
Over the last ten years, the consensus of multi-agent systems (MAS) has received increasing attention from mechanics, mathematics, physics, engineering sciences, social sciences, and so on. It is well known that the robustness of consensus of MAS is usually determined by several key factors, including noise, time-delays, and packet drop. In this paper, we introduce a general time-delayed MAS model with noise and also further investigate its robust consensus. In particular, we prove that the proposed algorithm is robust against the bounded time-varying delays and bounded noises. The effectiveness and robustness of the proposed consensus algorithm has been validated in the classical Vicsek model with time-varying delays. And two simulation examples are also given to justify the above theoretical results. These results may have some potential applications in various fields, including mechanics, biology, and engineering sciences.
