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

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


Contributed by: Housam Binous and Brian G. Higgins (March 2011)
Open content licensed under CC BY-NC-SA



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

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.