What are the possible concentration pathways for a 3-species system?
Of course, we can't display every pathway there is. We have to select a wide variety of rate constants to get a "good map" of the parameter-space. The approach I took was this:


Construct the differential equations


$$\frac{\mathrm dA}{\mathrm dt} = -k_1 A + k_3 C$$
$$\frac{\mathrm dB}{\mathrm dt} = -k_2 B + k_1 A$$
$$\frac{\mathrm dC}{\mathrm dt} = -k_3 C + k_2 B$$


Solve them numerically for every possible combination of 0.1, 1 and 10 for each rate constant and the above stated initial conditions
This leads to 27 pathways, which are plotted in a ternary diagram


The title of the ternary diagram is $k_1:k_2:k_3$, which is 0.1 : 0.1 : 0.1 in the first one.



(click for larger image)