  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.
