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Abstract Spontaneous synchronization is ubiquitous in natural and man-made systems. It underlies emergent behaviors such as neuronal response modulation and is fundamental to the coordination of robot swarms and autonomous vehicle fleets. Due to its simplicity and physical interpretability, pulse-coupled oscillators has emerged as one of the standard models for synchronization. However, existing analytical results for this model assume ideal conditions, including homogeneous oscillator frequencies and negligible coupling delays, as well as strict requirements on the initial phase distribution and the network topology. Using reinforcement learning, we obtain an optimal pulse-interaction mechanism (encoded in phase response function) that optimizes the probability of synchronization even in the presence of nonideal conditions. For small oscillator heterogeneities and propagation delays, we propose a heuristic formula for highly effective phase response functions that can be applied to general networks and unrestricted initial phase distributions. This allows us to bypass the need to relearn the phase response function for every new network. 

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.