  We investigated the locking behaviors of coupled limit-cycle oscillators with
phase and amplitude dynamics. We focused on how the dynamics are affected by
inhomogeneous coupling strength and by angular and radial shifts in the
coupling function. We performed mean-field analyses of oscillator systems with
inhomogeneous coupling strength, testing Gaussian, power-law, and brain-like
degree distributions. Even for oscillators with identical intrinsic frequencies
and intrinsic amplitudes, we found that the coupling strength distribution and
coupling function generated a wide repertoire of phase and amplitude dynamics.
These included fully and partially locked states in which high-degree or
low-degree nodes would phase-lead the network. The mean-field analytical
findings were confirmed via numerical simulations. The results suggest that, in
oscillator systems in which individual nodes can independently vary their
amplitude over time, qualitatively different dynamics can be produced via
shifts in the coupling strength distribution and the coupling form. Of
particular relevance to information flows in oscillator networks, changes in
the non-specific drive to individual nodes can make high-degree nodes phase-lag
or phase-lead the rest of the network.
