Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder
Active rotator models provide a minimal phase description of excitable and oscillatory systems, and have long been used to study mutual entrainment, synchronization, and collective transitions. Here, we investigate fully connected active rotator networks with Kuramoto coupling, where a common intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. This produces a competition between local pinning and collective phase alignment. Using mean absolute late-time drift and the fractions of positive and negative drifting oscillators, we construct numerical regime maps in the feedback-disorder-coupling plane. At weak coupling, increasing the feedback disorder strength suppresses drift, while stronger coupling can restore positive late-time drift when feedback disorder is not too strong. We interpret these regimes using analytical limits for the uncoupled and coherent strong-coupling cases. We also examine finite-size effects and zero-mean distributed intrinsic frequencies. Together, these results show that mixed-sign local feedback alone can reshape the balance between pinning and drifting in coupled active rotator networks, even when the intrinsic drive is homogeneous.