AI 中文总结
该研究基于 Kuramoto 同步模型构建数学模型，通过 Gamma 分布生成的单侧重尾噪声为连接分配随机动态权重，经数值实验和解析近似分析外部节点频率对同步转变点的影响。
AI 中文摘要
我们提出了一个数学模型，用于表示外部行动者（影响者）对一组行动者（受影响者）网络的影响。该模型是对 Kuramoto 同步模型启发的公式体系内控制系统的改进。我们将影响定义为改变他人特征或行为的能力，研究外部节点影响 Kuramoto 系统同步的能力，此时该系统的全局行为被拉向外部节点的频率，远离其自然平均频率。在本研究中，我们为网络与外部影响者之间的连接分配随机生成的动态权重，其中两个系统之间的连接通过 Gamma 分布生成的单侧重尾噪声进行分配。我们开展数值实验，考察外部节点改变受影响网络行为的能力的转变点：要么破坏同步，要么将其驱动至由外部节点确定的集体频率。我们研究了转变点对外部节点频率的依赖性，发现过高的驱动频率无法在保持同步状态的同时影响系统，而降低驱动频率则可实现偏离自然平均频率的同步状态。我们还研究了系统在同步和碎片化附近的解析近似，以理解其在该极限附近的行为。
英文摘要
We propose a mathematical model that represents the influence of an external actor (influencer) on a network of actors (influenced). The model is an adaptation of control systems within the family of formulations inspired by the Kuramoto Model of synchronisation. Capturing influence as a capacity to affect the character or behaviour of another, we study an external node's ability to influence the synchronisation of the Kuramoto system while its global behaviour is pulled to the external node's frequency and away from its natural mean frequency. In our work, stochastically generated dynamical weights assigned to the links between the network and the external influencer whereby links from one system to the other are assigned via one-sided heavy tail noise, generated by the Gamma distribution. We perform numerical experiments to examine transition points in the ability of the external node to alter the behaviour of the influenced network; either to disrupt synchronisation or to drive it to collective frequencies determined by the external node. We examine the dependence of transition points on the external node's frequency, where too ambitious a driving frequency fails to influence the system while retaining a synchronised state, and reducing achieves a state of synchronisation at a frequency shifted from the mean natural frequency. We also look at the analytic approximation for the system close to synchronisation and fragmentation to understand its behaviour around this limit.
Comments16 pages, 10 figures
