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arXiv · 2610.32739

Bistability with equal and independent removal in small bimolecular networks

Bo Peng
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Abstract

We classify two-species mass-action networks with at most three internal directed reactions on $\{X,Y,2X,X+Y,2Y\}$, positive inflows, and linear removal of both species. Among the 681 networks up to species exchange, exactly 27 admit two distinct positive hyperbolic attracting equilibria. The same 27 admit bistability with equal removal rates and with independently chosen positive removal rates. Each is minimal under reaction deletion. We give rational equal-removal witnesses for all positive cases and all-parameter exclusions for the remaining 654. The proof combines nullcline geometry, polynomial sign tests, resultant root bounds, and exact flux-cone decompositions. A separate rational-arithmetic implementation verifies the complete classification and its equilibrium certificates.

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Bo Peng. 2026-10-23. Bistability with equal and independent removal in small bimolecular networks. https://arxiv.org/abs/2610.32739

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