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

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].

dX

dt

dX

dt

dZ

dt

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].

t

α

β

γ

a

c

G(X)=a+cX

3

X

ac<0

a≠0

Thus with , , , the system becomes:

x=X+δ

y=Y+δ

z=Z+δ

dx

dt

3

(x-δ)

dy

dt

dz

dt

where , , represent concentrations of chemical species, with , . The chemical reaction scheme that leads to these equations is detailed in Table 1 of [2].

x

y

z

c=-0.143

δ=10