Figure 2.

Behaviour of N-gene oscillators. (a) Ratio of the probability of oscillations in an extended ring network with N + 1 genes and a genetic network of N genes for different values of the degradation rate of the N + 1th gene. In both cases explored N = 3 (blue) and N = 5 (green), the degradation of the N + 1th gene is varied while sampling the other degradation rates from the range δ_i = [10⁻³, 1] and keeping one random gene fixed at δ = 1. The other parameters and details of the sampling are the same as in figure 1c. (b) Frequency and amplitude of oscillations as a function of the network parameter A for 1000 successfully oscillatory networks from a random screening for different numbers of species with the same degradation rates δ_i = 1, N = 3 (red), N = 4 (blue) and N = 5 (green). Dashed lines and rings show the minimum critical value and angular velocity at that point α_m predicted by equations (2.13) and (2.14) for N = 3, 4, 5. The maximal values for A in the figure result from parameter sampling. In general A_max = (max ( Π_i f_i^'(x*))), which can be arbitrarily large. The repression functions are the same as in figure 1c with parameters logarithmically sampled from the intervals k_i : [10⁻⁵, 10⁻¹], a_i : [10⁻⁴, 10⁸], ρ^R_i : [10⁻⁴, 10⁴], ρ^A_i : [10⁻¹, 10¹¹], l_i : [10¹, 10⁵].