The Effect of the Frequency Inhomogeneity on the Synchronous States in Systems of Coupled Oscillators

Despite the ubiquity of systems with heterogeneous connectivity, the role of inhomogeneity on network synchronization has not been fully explored. We studied the effect of multiple inhomogeneities in coupling strengths and natural frequencies on the phase locking behaviors of coupled oscillators. In particular, we found that different Gaussian distributions in natural frequencies lead to diverse synchronization states of the coupled oscillator systems. With the stability analysis and numerical simulations, we analysed the transitions between synchronization states and its breakup in detail.