The Robertson model is a three-species mass-action system used as a test problem for solvers for stiff
differential equations (Robertson 1966, Baumgartner and Szmolyan 2025). If 
, 
, and 
are the concentrations, its ordinary
differential equations are
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
, 
, and 
are functions of time, primes denote derivatives
with respect to 
, and 
, 
, and 
are positive rate constants. The usual benchmark uses 
, 
, and 
, with initial
state 
.
Adding the equations gives the conserved total 
. The nonnegative concentrations with fixed 
form an invariant simplex,
so any concentration can be eliminated to obtain a planar system. Every solution
in this simplex tends to the equilibrium
point 
(Baumgartner and Szmolyan 2025). The widely separated rate constants make the approach
take place on different time scales.
