Amplified signal response by cluster synchronization competition in rings with short-distance couplings

Topological resonance has been revealed in degree-heterogeneous scale-free networks for weak signal amplification, but not in degree-homogeneous all-to-all networks [Acebrón et al., Phys. Rev. Lett. 99, 128701 (2007)0031-900710.1103/PhysRevLett.99.128701]. Here, we show that when the coupling distance of the all-to-all networks is reduced from global to local, i.e., converting all-to-all networks into rings, we can observe a resonant response to a weak signal similar to scale-free networks. We find that such a resonance effect induced by ring topology is robust across a wide range of ring sizes and signal frequencies. We further show that at intermediate coupling strength, oscillators in the rings can form separate synchronous clusters that compete with each other, resulting in large amplitude oscillations of boundary nodes between clusters and thus giving rise to the resonant signal amplification. Finally, we propose a structure of a three-node feed-forward motif simplified from the observed cluster synchronization competition to analyze the mechanism underlying the resonance behavior, which corresponds well with the numerical results.