Existing experiments demonstrated that constant light has either enhancing or diminishing effects on the behavioral rhythms of mammals, sparking our intense interest in the underlying mechanisms of this paradoxical phenomenon. The influence of constant light on behavioral rhythms involves the regulation of collective neuronal behavior. The robustness of behavioral rhythms stems from the synchronization of neurons. In mammals, the synchronization among neurons is regulated by the suprachiasmatic nucleus (SCN) located in the hypothalamus. Neurons within the SCN exhibit significant heterogeneity. The intrinsic frequency and coupling strength are two fundamental characteristics determining the internal dynamics of the SCN. In this study, the Poincaré model was employed to investigate the impact of constant light on SCN neuronal dynamics. We found that constant light can modulate neuronal synchronization, a phenomenon tightly linked to the critical threshold value of coupling strength among the neurons. Specifically, under weak coupling, constant light enhances neuronal synchronization. Under strong coupling, constant light weakens synchronization among oscillators. Furthermore, higher light intensity results in lengthened periods and reduced amplitudes. Our findings elucidate important underlying mechanisms by which constant light either enhances or diminishes mammalian behavioral rhythms, and provide a new perspective for understanding the complex regulation network of circadian rhythms. locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon locked icon Physics Subject Headings (PhySH)Collective dynamicsNeuronal dynamicsSynchronization