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. 2021 Mar 9;16(3):e0241654. doi: 10.1371/journal.pone.0241654

Fig 18. Response of oscillatory m2 controller with second-order autocatalytic generation of C and exponential increase of k1.

Fig 18

Phase 1 (0-40 time units): k1 = 2.0. Phase 2 (40-160 time units): k1 increases exponentially as shown in the left panel of Fig 3. Rate equations are given by Eqs 17, 2 and 10. Downward arrows indicate the starting point when the controller is able to compensate for the increasing k1 values. (a) A (in purple) and overall <A> (in green) as a function of time. The white outlined <A> is the <A> value calculated from 140 (white vertical line) to 160 time units showing that <A>= Aset = 5.0. (b) E as a function of time. (c) k1 and C as a function of time. (d) The period as a function of time. (e) High frequency oscillations near the end of phase 2. <A> is calculated for the time interval from 159.500 to 159.501 showing that <A> (4.9989) is close to Aset = 5.0. Rate constants: k2 = 1 × 105 (phase 1), k2 = 1 × 106 (phase 2), k3 = 5.0, k4 = 1.0, k5 = 5 × 10−2 (phase 1), k5 = 1 × 10−3 (phase 2), k6 = 1 × 10−3, KI = 1.0, KM = 1 × 10−6. Initial concentrations: A0 = 9.6, E0 = 55.4, C0 = 101.0, n = 4.