Resonance induced by higher-order coupling diversity

TL;DR

This paper introduces a novel way to incorporate higher-order coupling effects into linearly coupled systems, revealing that an optimal level of heterogeneity enhances signal response through a resonance phenomenon.

Contribution

It extends the concept of higher-order interactions to linear coupling systems using a new measure, enabling analysis of heterogeneous effects on signal propagation.

Findings

Optimal signal response occurs at intermediate higher-order coupling diversity.

Heterogeneous higher-order coupling can both promote and inhibit signal transmission.

Resonance arises from the balance between dispersion and aggregation effects.

Abstract

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.