Enhanced signal response through synchronization competition in a ring of four bistable systems

Recent research indicates that small-world networks can enhance weak signals through a phenomenon called topological resonance. However, the underlying mechanism of this effect remains unclear. In this study, we examine a ring of four bistable oscillators to analyze how it responds to an external subthreshold signal. Our findings reveal that the ring amplifies the signal via synchronization competition, where two desynchronized oscillators compete to synchronize with the other two, leading to increased oscillation and improved response to the subthreshold signal. Additionally, we find that synchronization competition is influenced by both the initial states of the oscillators and the characteristics of the subthreshold signal. We identify three synchronization transitions during signal amplification and propose three feedforward motifs to analyze the signal response of the ring. Finally, we apply the synchronization competition mechanism to explain the topological resonance of small-world networks.