FIGURE 6.

Semilog plot of β-galactosidase activity versus time showing effects of selection of the initial condition for t ∈[−τ, 0] in the numerical simulation with the parameters of Table 1 and various initial values of mRNA and allolactose oscillating around the unstable steady-state values corresponding to the middle branch of Fig. 2 when and L_e = 4.0 × 10⁻² mM (which is in the range of lactose concentration for coexistence of three steady states). The solid lines show the β-galactosidase activity when the initial allolactose functions are (n = 1, 2, …10), t ∈[−τ_M, 0], and the other variables are at the steady-state values on the middle branch. (Here is the unstable steady-state value of A on the middle branch). The dotted lines depict the temporal changes in β-galactosidase activity when (n = 1, 2, …10) for t ∈[−(τ_B + τ_P),0]. Again all the other variables are at the steady-state values when L_e = 4.0 × 10⁻² mM and is also the steady-state value of A on the middle branch. The steady-state values are , , , , and , when L_e = 4.0 × 10⁻² mM.