个体规则驱动的群体行为对称性破缺的临界状态

经济系统中,个体相互作用能够给群体涌现非常复杂的非线性行为,导致某些个体的非理性行为可能导致整个经济系统迅速崩溃,这种崩溃前系统的临界状态就显得异常重要.为了得到比较深刻的结论,将经济系统中个体之间的相互作用抽象成以随机复杂网络为结构的自适应博弈模型,从而构建合理的复杂自适应系统理论模型,然后通过随机攻击与蓄意攻击,来确定这一系统逾渗的临界状态.分析认为,当系统受到随机攻击时,系统表现出很强的鲁棒性,然而当系统受到蓄意攻击时,存在一个临界攻击概率使得系统具有较强的临界性.结论认为,系统受到随机攻击时,至少有两个大的组分保持系统联通,然而,当系统受到蓄意攻击时,系统存在一个临界删除概率,当删除概率小于这一临界概率时,系统存在两个大的组分;当删除概率大于这一临界概率时,系统难以保持联通.进一步而言,这一临界概率与系统中Agent的收益相关,这一结论修订了经典的以度为函数的复杂网络中的临界概率.

Criticality of symmetry breaking of collective behavior driven by individual rules

Agents' irrational behavior would lead to local configuration of complex adaptive system changed, which makes the system percolation, the criticality of system percolation is critical to make decision for improve the system or keep the system from being collapsed out of the blue and sharply. To draw a profound conclusion, a complex adaptive system model with agent's behavior and its local configuration co-evolved is constructed to describe how an arbitrary agent and its neighbors change their strategy and local interactive configuration, then the percolation critical point of this system can be gotten by considering it is attacked randomly and intentionally. It is shown that, after analyzing, the system is robust when it is attacked randomly, however, it is vulnerable when it is attacked intentionally. It is concluded that: when the system is attacked randomly, there are at least two large components keep the system connected in this system; however, when the system is attacked intentionally, the system has the critical point with deleting agents, which means that there are two large components keep the system connected in this system if the deleting probability is smaller than the critical probability and the system cannot be connected if the deleting probability is larger than the critical probability. Furthermore, the corresponding critical probability is driven by agents' payment, this conclusion revises the classic one decided by degree.