From chaotic itinerancy to intermittent synchronization in complex networks

Although synchronization has been extensively studied, key processes underlying its emergence in complex networks have remained hidden by the use of global order parameters. Here, we uncover how the route to synchronization unfolds through a sequential transition between two well-known but previously unconnected phenomena: (CI) and (IS). Using a symbolic dynamics approach, we show that CI develops as a collective yet unsynchronized exploration of different domains of the high-dimensional attractor of the network, whose dimension is reduced as the coupling increases, ultimately collapsing into the reference chaotic attractor of an individual unit. At this stage, the IS emerges as irregular alternations between synchronous and asynchronous phases. These phenomena are mutually exclusive, each dominating a distinct coupling interval and governed by different mechanisms. Furthermore, network structural heterogeneity enhances itinerant behavior since access to different domains of the attractor depends on the nodes’ topological roles. The CI-IS crossover occurs within a consistent coupling interval across models and topologies. Experiments on electronic oscillator networks confirm this two-step process, establishing a unified framework for understanding the route to synchronization in complex systems.