Figure 1.

Nonlinear chemical reaction network, featuring winner-take-all attractor dynamics. Crucially, all three high-concentration nonequilibrium steady states are symmetric with respect to exchanging X⁽¹⁾, X⁽²⁾, and X⁽³⁾. Thus, the associated minimum work-rate required (and the associated minimum driving concentration gradient $n\left(\mathrm{Hi}\right)-n\left(\mathrm{Lo}\right)$ to maintain each of these states is the same. (a) Layout of the chemical reaction network (b) Simulations of randomly initialized networks, with driving species clamped at $n\left(\mathrm{Hi}\right)=500, n\left(\mathrm{Lo}\right)=5$. Given this forcing, high-concentration states of an individual species ${\mathrm{X}}^{\left(1\right)}$, ${\mathrm{X}}^{\left(2\right)}$ or ${\mathrm{X}}^{\left(3\right)}$, as well as a low-concentration state are stable attractors of the dynamics. (c) Simulations of randomly initialized networks, with driving species clamped at $n\left(\mathrm{Hi}\right)=100, n\left(\mathrm{Lo}\right)=5$. Given this forcing, only the low-concentration state constitutes an attractor of the dynamics.