Figure 4. External weather-related light fluctuations are filtered out by limit cycle attractors but not by point attractors.

(a) Light intensity levels fluctuate on a range of time scales due to weather (power spectrum reproduced from Gu et al., 2001). (b) A population of limit cycle clocks of identical fixed geometry, subject to different realizations of weather conditions, show non-overlapping distributions (purple blobs) at different times of the day. Point attractor clocks form larger and more overlapping distributions. (c) A single representative dark pulse of $\sim 2.4$ duration causes only a $\mathrm{\Delta }\mathrm{\Phi }\sim 30$ min phase lag in limit cycles since the trajectory’s deviation (purple) is fundamentally bounded by the circular attractor. In contrast, $\mathrm{\Delta }\mathrm{\Phi }\sim 4$ hr for the point attractor since the trajectory is in free-fall towards the blue night-time attractor. (d) The geometrically computed $\mathrm{\Delta }{\mathrm{\Phi }}^2$ phase shift for a dark pulse of any fixed duration and time of occurrence (see Appendix 5) drops rapidly as ${(R/L)}^{-2}$ for large-$R/L$ limit cycles; this theoretical prediction agrees well with the population variance gain over a day in simulations. (e) Consequently, weakly driven limit cycles (i.e., high $R/L$) can tell time with high precision.