Synchronization and clustering across a population of genetic oscillators via attractive or repulsive coupling

Synchronization and clustering of genetic oscillators is a central topic in understanding rhythmicity of living organisms at both molecular and cellular levels. Here, we study two classes of genetic oscillators, i.e., relaxation genetic oscillator and regular genetic oscillator, coupled by attractive or repressive coupling, and show novel synchronization and clustering phenomena. We find that these two classes of coupled oscillators have the different mechanisms of synchronization and clustering in the cases of two kinds of couplings.