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Of Diamonds, Rings, and Bracelets: Local Values of the Response Parameter can Increase the Synchronization Probability in Pulse-Coupled Oscillators

Not all systems of pulse-coupled oscillators converge to synchrony from any initial configuration. The probability of synchronization depends on the network topology and the phase response function. It is often assumed that all oscillators are governed by the same phase response function. We exemplify that the synchronization probability can be significantly increased by using node-individual (local) values for the phase response parameter — rather than a single, global value. This insight motivates research into algorithms for parameter adjustment in self-organized network synchronization.