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.
In this paper, we investigate the nonlinear control problem for multi-agent formations with communication delays in noisy environments and in directed interconnection topologies. A stable theory of stochastic delay differential equations is established and then some sufficient conditions are obtained based on this theory, which allow the required formations to be gained at exponentially converging speeds with probability one for time-invariant formations, time-varying formations, and time-varying formations for trajectory tracking under a special"multiple leaders" framework. Some numerical simulations are also given to illustrate the effectiveness of the theoretical results.
