The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be straightforwardly extended to the linear ones. In present work, we introduce the standard deviation of dynamic behavior for the interacting group to complement the higher-order effect that beyond pairwise in diffusive coupling. By doing so, the higher-order effect can be flexibly extended to the linearly coupled system. We leverage this modelization to embrace the influence of heterogeneous higher-order coupling, including promoting and inhibiting effects, on the signal response for two conventional models, the globally coupled overdamped bistable oscillators and excitable FitzHugh-Nagumo neurons. Particularly, we numerically and analytically reveal that the optimal signal response can be obtained by an intermediate degree of higher-order coupling diversity for both systems. This resonant signal response stems from the competition between dispersion and aggregation induced by heterogeneous higher-order and positive pairwise couplings, respectively. Our results contribute to a better understanding of the signal propagation in linearly coupled systems.

中文翻译：

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由高阶耦合分集引起的共振

由高阶相互作用引起的集体振荡的研究指出了耦合建模中群效应的必要性。迄今为止，相关进展主要集中在非线性耦合模式上，不能直接扩展到线性耦合模式。在目前的工作中，我们引入了相互作用组的动态行为的标准偏差，以补充扩散耦合中超出成对的高阶效应。通过这样做，高阶效应可以灵活地扩展到线性耦合系统。我们利用这种建模来包含异构高阶耦合的影响，包括促进和抑制效应，对两个传统模型的信号响应，即全局耦合过阻尼双稳态振荡器和可兴奋 FitzHugh-Nagumo 神经元。特别，我们在数值和分析上表明，可以通过两个系统的中等程度的高阶耦合多样性来获得最佳信号响应。这种共振信号响应源于分别由异质高阶和正成对耦合引起的分散和聚集之间的竞争。我们的结果有助于更好地理解线性耦合系统中的信号传播。