The Oregonator is a nonlinear dynamical system of three first-order ordinary differential
equations modeling concentration oscillations in the Belousov-Zhabotinsky reaction
(Field and Noyes 1974). In dimensionless variables 
, 
, and 
, it is
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
, 
, 
,
and 
are positive constants and the derivatives
are with respect to dimensionless time (Field 2007). The vector
field points inward or is tangent on each boundary face of the nonnegative octant, so initially nonnegative concentrations remain nonnegative.
At a positive equilibrium point, 
and 
. Substituting into
the first equation gives
 |
(4)
|
The negative constant term ensures that the two roots have opposite signs. The positive root therefore determines the unique positive equilibrium point.
Field and Noyes (1974) numerically found an attracting limit cycle for a parameter choice equivalent to 
, 
, 
,
and 
in this scaling.
The trajectory in phase space approaches the same
cycle from several different sets of initial conditions.
