Fig. 5.

Limit-cycle model of the circadian pacemaker. (A) A 2D limit cycle oscillator is represented diagrammatically by a circle that represents the steady-state path of the oscillatory system. In this rendition, time moves clockwise around the circle, and four phase points are indicated by the radial lines that represent “isochrons,” or sets of points with equivalent phase (26). The singularity, which is an unstable equilibrium point, is indicated by the black dot at the intersection of the isochrons. The blue vectors represent the perturbations caused by light pulses. During the perturbation, the system is carried off the limit cycle to a point in phase space indicated by the arrow. The dotted blue circle represents the set of points to which light would send the system at all possible phases of the cycle. In this diagram, vectors for only two examples are shown. The new phase of the system can be determined by the isochrons. The perturbed system would relax back to the limit cycle as it reaches steady state. In A, the strength of the light pulse is weak, and pulses cannot push the system across the singularity to the opposite phases of the cycle. Thus, new phase is similar to old phase and the resetting is Type 1. (B) The limit cycle is the same as that shown in A; however, the strength of the light input is strong and, therefore, the light can push the system across the singularity to the opposite side of the limit cycle, which results in very large phase shifts or Type 0 resetting. The stronger effect of light is represented by a larger (longer) vector. (C) In this limit cycle, the amplitude has been reduced by 30% and is represented by a limit cycle with a smaller diameter. Here the effect of light is the same as in wild type (the vector is the same size), but light now is strong enough to carry the system across the singularity to cause large phase shifts and Type 0 resetting.