Exploration of brain dynamics patterns has attracted increasing attention due to its fundamental significance in understanding the working mechanism of the brain. However, due to the lack of effective modeling methods, how the simultaneously recorded LFP can inform us about the brain dynamics remains a general challenge. In this paper, we propose a novel sparse coding based method to investigate brain dynamics of freely-behaving mice from the perspective of functional connectivity, using super-long local field potential (LFP) recordings from 13 distinct regions of the mouse brain. Compared with surrogate datasets, six and four reproducible common functional connectivities were discovered to represent the space of brain dynamics in the frequency bands of alpha and theta respectively. Modeled by a finite state machine, temporal transition framework of functional connectivities was inferred for each frequency band, and evident preference was discovered. Our results offer a novel perspective for analyzing neural recording data at such high temporal resolution and recording length, as common functional connectivities and their transition framework discovered in this work reveal the nature of the brain dynamics in freely behaving mice.