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