A set of Python files that can be used for the numerical and qualitative analysis of the Oregonator model. This simple model can be used to describe some of the chemical kinetics that occur during the famous Belousov-Zhabotinsky reaction.
The Belousov-Zhabotinsky reaction is an unusual reaction which depicts the sustained oscillation of the concentration of chemical species that are involved. In the order I used them, the files consist of:
- Numerical solutions.
- Phase portraits.
- A parameter plot.
- Nullcline (zero derivative values) plot.
- A bifurcation plot.
- Eigenvalue computations.
I created this code for the 3rd year project of my Maths degree. I enjoyed this so much that I would prefer to share it with others.
My hope is that this code could be used to:
- Help teach about numerical ODE solving in Python.
- Explore the wonderful applications of Dynamical Systems Theory in practice.
- Last but not least, demonstrate the wide variety of applications Mathematics has beyond Biology and Physics.
I also would be intrigued to see if anyone would extend this analysis to the multivariate Oregonator model which features a Laplacian term in both differential equations and switches to plane polar coordinates.
The core reference for this is Scott's Oscillations, Waves and Chaos in Chemical Kinetics (1994).
This code features an extensive use of the numpy and matplotlib modules.