A Reset Algorithm Solving Coordination With Antagonistic Reciprocity
提出一种由线性脉冲动力学构成的重置算法，解决个体间存在对抗互惠时的协调问题，统一了共识、聚类和稳定性三种情形。
This article is dedicated to solving the coordination problem using a reset algorithm that consists of linear impulsive dynamics, over which antagonistic reciprocity among interacting individuals is inevitable. It shows that reciprocal agents are convergent (including consensus and clusters) whenever the scaling parameters of an agent, corresponded to continuous/discrete dynamics, enjoy the same proportion value that matches to all agents. Otherwise, all participating agents share nothing eventually, that is, they achieve stability. This immediately gives rise to that the final aggregated values of agents are entirely determined by the underlying parameters, on condition that the connection property of communication topologies is preserved. Therefore, the proposed setup features a unified perspective on consensus, clusters (including bipartite consensus), and stability that are separately studied in most of the existing literature. The developed method is well supported via numerical examples.