论文标题
定期耦合抑制网络上的二阶共识
Periodic Coupling inhibits Second-order Consensus on Networks
论文作者
论文摘要
近年来，网络上的共识算法已受到越来越多的关注，从动物植入到多车的协调范围。在建立的多代理网络二阶共识的既定模型的基础上，我们通过相当小的时间周期性耦合调制调制来揭示了一种抑制集体共识状态形成的机制。我们在光谱分解中处理该模型，并分析地发现，对于某些中间耦合频率，参数共振是在网络级别诱导的 - 与预期的非常短的和长时间耦合时间尺度的共识的出现不符。我们的形式主义准确地预测了这些共振频率，并将它们与静态骨干网络的拉普拉斯频谱联系起来。系统的激发是在参数共振理论中量化的，我们通过时间周期性耦合将其扩展到网络域。
Consensus algorithms on networks have received increasing attention in recent years for various applications ranging from animal flocking to multi-vehicle co-ordination. Building on the established model for second-order consensus of multi-agent networks, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations. We treat the model in its spectral decomposition and find analytically that for certain intermediate coupling frequencies parametric resonance is induced on a network level -- at odds with the expected emergence of consensus for very short and long coupling time-scales. Our formalism precisely predicts those resonance frequencies and links them to the Laplacian spectrum of the static backbone network. The excitation of the system is furthermore quantified within the theory of parametric resonance, which we extend to the domain of networks with time-periodic couplings.
