FIGURE 3.

Dynamic characteristics of the original three-node repressilator (top row) and the four-node extended repressilators a–d. The phase diagram in (α, β) parameter space with α₀/α = 10⁻³ and n = m = 2 is shown for each oscillable configuration and regulation function, both in linear and logarithmic scales, for clarity. Labeling of the panels follows that of Fig. 1. The configuration b is not shown since it does not support the sustained oscillations for any parameter set investigated. The configuration d is shown for each of the regulation functions of the form F^S (fourth row) and F^I (fifth row). The gray region in the phase diagram indicates the cases where the sustained oscillation occurs in the extended system and the region enclosed by the black-dotted curve denotes the cases where the sustained oscillation occurs in the original three-node repressilator, shown for comparison. Also shown is the temporal profile of the continuous modeling with the parameters α = 20 and β = 0.4 (marked by “×” in the phase diagram). Each curve shows the profile of the node N1 (red solid), N2 (orange dashed), N3 (blue dotted), and N4 (cyan dash-dotted), respectively. Note that trajectories of N3 and N4 overlap in d. Typical temporal profiles for the corresponding Boolean dynamics are shown in the rightmost column. The color-coding of the Boolean dynamic profiles follows that of the continuous modeling.