Bridge-module-induced unihemispheric-sleep-like oscillations on connected excitable complex networks

The introduction of a bridge module between multiple networks may bring forth new possibility of collective dynamical behaviors. In this paper, by exploring the sustained oscillatory behaviors of bridge-module-connected excitable networks, a double-oscillation mode can self-organize to emerge besides the single-mode oscillation mode, where one network performs fast-active-waves oscillation while the other implements slow-sleep-waves oscillation. This behavior is similar to the unihemispheric sleep phenomenon widely observed in birds and aquatic mammals, and is consequently named as the unihemispheric-sleep-like oscillation (USLO). By utilizing the dominant phase-advanced driving (DPAD) method, the loop structure is demonstrated as the oscillation source in maintaining the USLOs. More profoundly, an effective-driving analysis approach (EDAA) is proposed to unveil the mechanism of the USLOs. The bridge-module-induced instability of the original 1:1 response mode is shown as the determinant in inducing the USLOs on the bridge-module-connected excitable networks. Furthermore, the bridge-module-induced USLOs on multiple connected excitable networks are found to be universal. The method and results demonstrated in the present paper can give us clues in understanding the amazing phenomenon of unihemispheric sleep emerging in highly complex and heterogeneous brain network systems.