Phase frustration is often used to represent an effective phase lag caused by signal transmission, sensing, processing, or response delays. In conventional phase-oscillator models, a fixed phase lag usually weakens the attractive component of the coupling and tends to hinder synchronization. Here we show that, when phase frustration is adaptively regulated by the collective state, it can instead provide a feedback mechanism for hysteretic synchronization transitions. In many oscillator populations, the effective phase lag need not remain fixed. When coherence is weak, the collective rhythm is difficult to predict and the effective phase mismatch can be large. When coherence grows, the rhythm becomes more predictable, so feedback or phase correction may reduce this mismatch. Motivated by this physical picture, we consider a population of globally coupled phase oscillators in which the frustration angle decreases with the global order parameter. This adaptive phase frustration creates a positive feedback between growing coherence and the effective attractive interaction. Numerical scans show that this feedback can change a continuous transition into a hysteretic jump with coexisting coherent states. The transition persists when the feedback exponent and frequency width are varied, remains visible in finite-size tests, and can also appear in networked systems. For the globally coupled Lorentzian case, the Ott-Antonsen reduction gives a low-dimensional explanation of the coherent branch and the forward and backward transition points. These results show that adaptive regulation of phase frustration provides a physically motivated phase-lag feedback mechanism for bistability and hysteretic synchronization transitions.

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• Synchronization transition
• Collective dynamics
• Coupled oscillators