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We demonstrated, both numerically and analytically, that the critical synaptic strength and the network average degree obey a power-law relation with an exponent of -1. Our study provides a possible dynamical network mechanism of the transitions between tonic and bursting neural activities for the wakefulness-sleep cycle, and of the SWA during sleep. Further interesting and challenging investigations are briefly discussed as well.The present paper analytically reveals the effects of frequency mismatch on the stability of an equilibrium
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