{"id":"palomar/PALOMAR-2026-10-11-000011","url":"https://github.com/mmislan/palomar-shared-resource-realizations/tree/d985d04a6cee575f8ac6dc32db98a390393d9b39","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-11-000011-v1.json","repo":"https://github.com/mmislan/palomar-shared-resource-realizations","tags":["math.DS","q-bio.MN","msc:34D20","msc:37N25","msc:92C42","mass-action-kinetics","reaction-networks","dynamical-systems"],"score":0,"title":"Realizations and dynamics of shared-resource mass-action systems","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Ordinary mass-action realizations are characterized for a finite family of two-species modules coupled through a shared resource and buffer. Every positive parameter vector admits a strongly connected realization of the same polynomial field. A complex-balanced realization at a prescribed positive state exists exactly when the state is stationary and two explicit local flux inequalities hold, even when arbitrary finite auxiliary complexes on the same species are allowed. An explicit endpoint sign test determines the untransported heterogeneous parameter locus, and the state criterion extends…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-11","reactions":{},"formalized":true,"formalizes":[{"title":"Realizations and dynamics of shared-resource mass-action systems","identifier":"","relationship":"formalizes"}]}