Partial Phase Cohesiveness in Networks of Communitinized Kuramoto Oscillators

Partial synchronization of neuronal ensembles are often observed in the human brain, which is believed to facilitate communication among anatomical regions demanded by cognitive tasks. Since such neurons are commonly modeled by oscillators, to better understand their partial synchronization behavior, in this paper we study community-driven partial phase cohesiveness in networks of communitinized Kuramoto oscillators, where each community itself consists of a population of all-to-all coupled oscillators. Sufficient conditions on the algebraic connectivity of the \textit{selected communities are obtained to guarantee the appearance of their phase cohesiveness, while leaving the remaining communities incoherent. These conditions are further reduced to the form of the lower bounds on the coupling strengths for the connections linking the selected communities. We also show that the ultimate level of the phase cohesiveness that the oscillators asymptotically converge to is predictable. Finally, numeral studies are performed to validate the obtained results.