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Nature and relations of the incoherence transition in heterogeneous Stuart–Landau ensembles

Analyze the transition from frequency synchronization to incoherence in globally coupled heterogeneous Stuart–Landau oscillator ensembles; determine whether the transition is discontinuous, identify the critical coupling Kc, and assess its relation to recently reported synchronization transitions such as explosive or extreme synchronization.

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Background

The authors state that numerical evidence indicates a discontinuous loss of frequency synchronization when the coupling strength K decreases below a critical value Kc in the heterogeneous Stuart–Landau ensemble. However, a comprehensive analysis of this transition is lacking.

They further propose investigating the potential connections between this transition and other abrupt synchronization phenomena reported recently, which would situate their observations within the broader landscape of synchronization theory.

References

This work raises several open questions. Moreover, it would be important to analyze the transition into incoherence for the heterogeneous system of globally coupled SL oscillators~eq:SLGC_het. Numerical evidence suggests that there is a discontinuous transition off frequency synchronization as K is decreased past a critical parameter Kc. In this context, it is interesting to investigate how far it is related to more recently reported synchronization transitions.

— Complete Synchronization and Pattern Selection through Amplitude Dynamics and Diffusion in Heterogeneous Oscillatory Media (2510.06083 - Thomé et al., 7 Oct 2025) in Section 5 (Conclusion and Outlook)