Synchronization enhancement by dissipative coupling.

We investigate how the nature, rather than just the strength, of coupling controls synchronization between self-sustained oscillators. By parametrizing the coupling between two van der Pol oscillators as Je^{iθ} at fixed overall strength J, we continuously tune from purely coherent (θ=0) to purely dissipative (θ=π/2) coupling. We find that dissipative coupling yields a substantially wider frequency-locking window than coherent coupling in both the weakly and strongly nonlinear regimes. In the weakly nonlinear regime, hybrid coherent-dissipative coupling unlocks an unbalanced synchronization (U-sync) regime with strongly asymmetric amplitudes, extending the locking window far beyond the conventional balanced-synchronization (B-sync) boundary. A systematic bifurcation analysis, supported by Matcont numerical continuation, identifies the synchronization boundaries as saddle-node bifurcations in the strongly nonlinear regime for all coupling angles, and as saddle-node (for purely dissipative coupling) or Hopf (otherwise) bifurcations in the weakly nonlinear regime. We confirm the predicted synchronization enhancement and both the B-sync and U-sync regimes experimentally using coupled self-sustained LC resonators with tunable coherent-dissipative coupling. Our results establish the coupling angle as a practical tuning knob for synchronization engineering and suggest design principles, based on the dissipative-to-coherent ratio of each pairwise link, for controlling synchronization robustness and amplitude distributions in oscillator networks.