Partial synchronization and its applications to brain networks

Synchronization represents one of the key topics in nonlinear dynamics and complex networks for many decades, because of its potential applications in many real-world systems, especially the abnormal synchronization of the human brain. Over the past decade, the attention has shifted to the phenomenon of partial synchronization on complex networks, where only a part of the network units displays a synchronized behavior, while the rest of the network evolves in an unsynchronized manner. Typical partial synchronization phenomena include chimera states, cluster synchronization, and remote synchronization, which aim to explain the complicated mechanisms of brain functions. On the other hand, signal propagation in complex networks has recently also attracted much attention, as it may reveal the underlying mechanisms of various partial synchronized patterns. In this direction, a wealth of important results have been obtained, such as the topological resonance, coupling resonance, and even remote propagation. More and more experiments have been designed to confirm these findings. In sum, these results open a new avenue to understand the mechanisms of brain functioning, including both the normal and abnormal brain functioning. Thus, our intention is to offer here a monographic review of the mainstream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.