Traveling chimera states by weak temporal couplings

The mechanisms of self-sustained oscillations of brain rhythms have been studied for a long time and it is revealed that the emergence of a pacemaker loop takes a key role for these rhythms. However, it is unclear how this pacemaker loop plays a role in the resting state of the brain, where the characteristic slow-wave activities show a multi-scaled feature and can switch easily between different dynamics states. To study this problem, herein we present a neural model of pacemaker looplike network, with a weak temporal electrical coupling to mark the resting state of the brain. We find that different dynamics patterns can be generated by this model, including the disorder, traveling chimera state, chimera state, and synchronization. Interestingly, we observe a sensitive switching effect between the region of traveling chimera state and that of chimera state, which may provide new insights to the mechanism of quickly switching between different rhythms of the brain in the resting state. Further, we introduce an index Q to describe the fluctuations of the local order parameter of network and conjecture that there is a new regularity caused by the fluctuations. We find that Q is optimally dependent on the matching of parameters and thus confirms the conjecture. Moreover, we show that the observed traveling chimera state is robust to different forms of temporal couplings.