Mechanism of phase splitting in two coupled groups of suprachiasmatic-nucleus neurons.

The phase-splitting behavior of coupled suprachiasmatic-nucleus neurons has been observed in many mammals, and its mechanism is still not completely understood. Based on our previous work [C. Gu, J. Wang, and Z. Liu, Phys. Rev. E 80, 030904(R) (2009)] on the free-running periods of neurons in the suprachiasmatic nucleus, we present here a modified Goodwin oscillator model to explain the mechanism of phase splitting. In contrast to the previous phase model, the modified Goodwin oscillator model contains the information on both the phase and amplitude and, thus, can show more features than the purely phase model, including all three behaviors of synchronization, phase splitting, and amplitude death and the distributed periodicity in the regions of synchronization and phase splitting, etc. An analytic phase model is extracted from the modified Goodwin oscillator model to explain the dependence of periodicity on the parameters. Moreover, both the modified Goodwin oscillator model and the analytic phase model show that the ensemble frequency can be enhanced or reduced by the time delay.