Mirroring of Synchronization in Multilayer Configuration of Kuramoto Oscillators

One of the most fundamental and important emergent phenomena observed in complex systems is synchronization [1], where the smaller parts of the larger coupled system behave in unison. Other fascinating phenomena in such systems include explosive transitions [2–5], chimeras [6, 7], amplitude death [8, 9], and so on. In these systems, it is possible to observe the simultaneous occurrence of emergent phenomena, such as synchronization, in distinctly different parts of the system. One example is “contagious yawning” where observing one individual yawn will trigger yawning in others. This has been observed across species [10–12] and is thought to be due to the synchronous activation of the mirror neuron system in the brain, which is triggered by observing specific actions [13]. This suggests that there is a section in the brain that mirrors the dynamics of what is visually observed from another individual. Other examples include fake news propagation and jamming in communication networks.