Steady-States of a Nonlinear Chemical System Using the Arc Length Continuation Method

Consider the following nonlinear chemical reaction scheme:
One can show that this nonlinear chemical system obeys the nondimensionless equation:
, where is the dimensionless concentration of species and is dimensionless time.
This Demonstration shows the steady-state values versus for user-set values of . As can be seen from the snapshots, this plot has the characteristic -shape. The two turning points are computed and indicated by the green dots. For some values of there are three steady states. A stability analysis can show that only two of these are stable.

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DETAILS

G. Nicolis, Dynamique Chimique, Thermodynamique, Cnétique et Mécanique Statistique, Paris: Dunod, 2005.
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