Consensus algorithms on networks have received increasing attention in recent years for various applications, ranging from distributed decision making to multivehicle coordination. In particular, second-order consensus models take into account the Newtonian dynamics of interacting physical agents. For this model class, 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.

中文翻译：

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周期性耦合抑制了网络的二阶共识

近年来，网络上的共识算法在从分布式决策到多车协调的各种应用中受到越来越多的关注。特别是，二阶共识模型考虑了相互作用的物理主体的牛顿动力学。对于此模型类，我们揭示了一种通过相当小的时间周期耦合调制来抑制集体共识状态形成的机制。我们在模型的频谱分解中对其进行处理，并通过分析发现，对于某些中间耦合频率，参数共振是在网络级别上引起的，与预期的非常短和长耦合时间尺度的共识出现不一致。我们的形式主义精确地预测了那些共振频率，并将它们与静态骨干网络的拉普拉斯谱联系起来。