Figure 2
Multi-dimensional dynamics analysis of the Goodwin system with negative feedback.
(a) Kinetic diagram of the Goodwin system. (b) Time-course simulation of sustained oscillations exhibited by the Goodwin system. (c) 2-D bifurcation diagram for parameters kd1 vs. kd2. Red indicates region of oscillation while grey indicates region of monostable fixed point. Parameters used are: k1 = k2 = k3 = 0.1 (nM s−1), kd3 = 0.01 (s−1), n = 9, K = 1 (nM). (d) PC-based bifurcation diagram for parameters kd1 and kd2. The remaining parameters values are as in (c). The sampling ranges for respective parameters are given on top of each vertical axis. All parameter values are normalised to the [0,1] interval. Note that the same notation applies hereafter for other PC plots. (e) PC-based bifurcation diagram for parameters kd1, kd2 and kd3. The remaining parameters values are as in (c). (f) PC-based bifurcation diagram for kd1, kd2, kd3 and K, n. The remaining parameters values are as in (c). Here, only the oscillation sets are displayed for clarity; the red lines indicate the sets with strong negative feedback (K < 0.1) while blue lines indicate those with weak feedback loop (K > 0.1). (g) PC-based bifurcation diagram for the rates of synthesis and degradation. The red lines indicate the sets giving oscillations while blue lines indicate monostable sets. The remaining parameters values are as in (c).
