Second-order interactions induce anti-phase synchronization between the left and right suprachiasmatic nucleus

Abstract

In the dynamical study of neural networks, pairwise coupling has long been regarded as the classical paradigm for describing interactions between neurons. However, recent studies have revealed the existence of more complex higher-order interactions among neurons, and this group coupling pattern often induces collective behaviors that cannot be explained by traditional models. As the core regulator of circadian rhythms, the suprachiasmatic nucleus (SCN) exhibits a splitting phenomenon under specific conditions, which is characterized by anti-phase synchronization between the left and right nuclei. The underlying dynamical mechanisms of this phenomenon remain an open question. This article aims to explore this issue from the perspective of higher-order interactions. Based on a higher-order Kuramoto model with phase-shifts, we investigated the effect of second-order interactions on the collective behaviors of the SCN networks. The results demonstrated that when both the first-order and second-order phase shifts exceed π / 2 , second-order interactions of appropriate strength can directly induce the splitting phenomenon. Our findings reveal the role of higher-order interactions in the split of coupled neuronal oscillators, offering new insights into the collective dynamics of circadian rhythms.