Category: Nonlinear Dyn.

Summary: Testing whether delayed adaptive pinning can improve synchronization resilience in a multiplex Kuramoto network before control fatigue erodes the benefit.

Synchronization in coupled oscillator systems can often be improved by pinning or controlling selected nodes, but the value of intervention depends on both timing and fatigue. This experiment asks whether multiplex oscillator networks have a re-entrant delay window where adaptive pinning outperforms static control.

The script constructs random graph layers, evolves coupled phase dynamics, and compares adaptive and static strategies across delays. It records resilience gains, fatigue gaps, and the delay that maximizes improvement, with particular attention to whether the middle of the delay range beats the edges.

That makes the experiment relevant to overloaded networked systems where intervention weakens with repeated use. The result is not just a synchronization score, but a timing map of when control remains effective.

Method: Kuramoto dynamics on multiplex random networks with delayed adaptive pinning, compared against static control and summarized by re-entrant gain metrics.

What is measured: Re-entrant index, mid-window gain, edge gain, best delay, adaptive versus static resilience, fatigue gap, and support fraction for the timing hypothesis.