2882
Additions and Corrections
The Journal of Physical Chemistry, Vol. 85, No. 19, 1981
OREGONATOR
Figure 1. Computer-produced projections of the three-dimensionai limit cycle for the first 75 s (approximately 8 cycles) of the Oregonator of ref 1. The symbols mark the following times (in seconds) on the plot: n, 1 x 0,1 x 10-4; A, 1 x io-? +, 1 x IO-*;X, 1 x io-’; 0 , 1; v, 10.
The duration of this transient is dependent on the initial conditions and its presence could lead to an error in our calculations. In principle we agree with Fife’s analysis. It is necessary to assure that the transient has died out (to within a sufficient numerical accuracy) by the smallest time used
in the sensitivity calculation. Fife presents an expression for the transient correction term, It would be possible to evaluate this, or, as Fife suggests, to make additional calculations of & / d a as a function of time until a constant value is obtained. The former would involve the additional computation of the sensitivity of the oscillating component used for the analysis ([Z] for the Oregonator) to the initial [Y], concentrations of all the oscillating components ([XI, [Z]). Extending the computation of & / d a to longer times would require a deeper probe into the sources of error involved in integrating the Green’s function kernel, as mentioned in our paper.l A more practical approach is to examine the numerical values of the solution vector to ascertain that they recycle accurately at the times used. Figure 1is a plot of the limit cycle of the Oregonator for the rate constants and initial conditions used in ref 1. Despite the apparent large distance between the initial conditions and the limit cycle (greatly distorted on the expanded logarithmic scale) the limit cycle is reached within 1ms of real time, and thereafter is retraced to much better precision (
