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].

[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.