脉冲耦合振荡器在环形图网络中的全局同步
Global Synchronization of Pulse-Coupled Oscillators Interacting on Cycle Graphs
AI总结：
研究脉冲耦合振荡器在环形图网络中的全局同步问题，发现环形网络中振荡器数量增加时需增强耦合强度以保证同步，且单向环形网络中需考虑相位响应曲线的不应期以实现全局同步。
摘要：
脉冲耦合振荡器（PCOs）在生物和工程中的重要性推动了对其网络基本性质的研究。尽管已有大量关于PCOs的研究，但针对比全连接网络更一般化的网络的全局同步结果仍然缺失。本文研究了由环形图描述的PCO网络的全局同步问题。对于双向环形网络，当环中振荡器数量增加时，必须增加耦合强度以保证任意初始条件下的同步。对于单向环形网络，最强耦合无法保证全局同步，但相位响应曲线中的不应期足以实现全局同步。分析结果通过数值模拟得到验证。
英文摘要：
The importance of pulse-coupled oscillators (PCOs) in biology and engineering has motivated research to understand basic properties of PCO networks. Despite the large body of work addressing PCOs, a global synchronization result for networks that are more general than all-to-all connected is still unavailable. In this paper we address global synchronization of PCO networks described by cycle graphs. It is shown for the bidirectional cycle case that as the number of oscillators in the cycle grows, the coupling strength must be increased in order to guarantee synchronization for arbitrary initial conditions. For the unidirectional cycle case, the strongest coupling cannot ensure global synchronization yet a refractory period in the phase response curve is sufficient to enable global synchronization. Analytical findings are confirmed by numerical simulations.
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