Figure 5. Entrainment to periodically applied 2-h dark pulses.

(a–d) Bioluminescence signals of the CCA1::LUC plant perturbed by 2-h dark pulses with a period of (a) T = 22 h, (b) T = 25 h, (c) T = 18 h, and (d) T = 32 h. Each panel represents the averaged signal over n = 30, 22, 20 and 9 plants, respectively. Gray bars indicate timing of 2-h dark pulses. (e, f) Return maps of phase Φ_k observed at the kth dark pulse under T = 22 h (e) and 25 h (f). The points were obtained from (a) and (b). The red squares and blue triangles indicate transient processes to approach the stable fixed point with increasing and decreasing direction of Φ_k, respectively. The solid lines indicate Φ_k+1 = Φ_k + G(Φ_k) + 2π(T − τ)/τ mod 2π with a natural period of τ = 23 h. The open circle and cross represent stable and unstable fixed points, respectively, obtained as solutions of G(Φ) + 2π(T − τ)/τ = 0. (g, h) Time series of the phase Φ_k under (g) T = 18 h and (h) T = 32. The points were obtained from (c) and (d).