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Figure 5.9. Logistic map with /i = 3.83 results in a three-period orbit.

continuous stirred tank reactors fed with a volumetric flow rate /, and a coupling strength g, as shown in Figure 5.10, we can write the material balance equations as dr'

where r, is the resource concentration in the ith tank, ro is the resource concentration in the feed, pl is the concentration of species P in the ith tank, and % = 1,2, j = 1, 2 with i ^ j.

Investigating a species P with kp = 25 and dp = 0.1 in a setup with concentration, ro = 1 and coupling strength g = 0.002, we can use the feed flow rate / as a bifurcation parameter to plot the bifurcation diagram of

Figure 5.11. For / = 0.006728, we get the chaotic trajectory of Figure 5.12.

Figure 5.10. Two coupled identical CSTRs with cubic autocatalytic species P.

r2'P2

Figure 5.10. Two coupled identical CSTRs with cubic autocatalytic species P.

0.0066 0.0068 0.007 0.0072 0.0074 f

Figure 5.11. Bifurcation diagram of the autocatalytic species P, showing the stable steady states (thick curve), the unstable steady states (thin curve), and the stable limit cycle (dotted curve), using the feed flow rate, / as the bifurcation parameter.

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