A Chaotic Chemical Reaction Scheme Derived from Chua's Circuit Equations

This Demonstration plots the solution of Chua's equations describing a chemical reaction scheme analogous to Chua's electrical circuit. Chua's circuit is the simplest electronic circuit that exhibits classic chaotic behavior [1].
where is time; , , , , and are parameters; and is a cubic equation with , . The solution to these equations allows both positive and negative values of the variables. A linear transformation of variables can convert this electrical system into a dynamically related chemical scheme that allows only positive state variables [2].
Thus with , , , the system becomes:
where , , represent concentrations of chemical species, with , . The chemical reaction scheme that leads to these equations is detailed in Table 1 of [2].


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


[1] A. Huang, L. Pivka, C. W. Wu, and M. Franz, "Chua's Equation with Cubic Nonlinearity," International Journal of Bifurcation and Chaos, 6(12), 1996 pp. 2175–2222. doi:10.1142/S0218127496001454.
[2] Q. S. Li and W. Xu, "A Chemical Model for Chua's Equation," International Journal of Bifurcation and Chaos, 12(4), 2002 pp. 877–882. doi:10.1142/S0218127402004760.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+