Inspired by [this question](https://chemistry.stackexchange.com/questions/15511/can-a-multi-species-system-oscillate-around-equilibrium), which asks if a multi-species system could oscillate around its equilibrium, I thought about the possible concentration pathways the following more narrow specified system could take:

$$ \ce{A ->[\text{$k\_1$}] B} $$
$$ \ce{B ->[\text{$k\_2$}] C} $$
$$ \ce{C ->[\text{$k\_3$}] A} $$

What I was interested in are the ratio of those concentrations $A:B:C$. The initial conditions are $A(0)=1$, $B(0)=0$, $C(0)=0$. (For simplicity, $[\ce{A}] \equiv A$, and analogous for $B$ and $C$)

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> What are the possible concentration pathways for different values of $k\_1$, $k\_2$ and $k\_3$?
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