Practical incorporation of strong coupling effects in coupled oscillator models

Develop practical methodologies to incorporate strong coupling effects into phase-based descriptions of delay-coupled oscillator networks so that the modeling framework remains valid beyond the weak-coupling limit and can accurately capture synchronization transitions and their criticality.

Background

The paper studies synchronization transitions in coupled oscillator networks and highlights that predictions derived from weak-coupling phase reductions can break down as coupling strength increases. In real systems, strong coupling can alter the criticality of bifurcations (continuous versus discontinuous transitions) and involve amplitude dynamics that are not captured by first-order phase models.

Recent developments include higher-order phase reductions and phase–amplitude reductions, including for systems with time delay. While these approaches have shown promise, they are typically ad hoc and lack rigorous justification. Within this context, the authors explicitly point out that a central unresolved issue is determining how best to incorporate strong coupling effects in a practical modeling framework.