{"id":"palomar/PALOMAR-2026-10-11-000020","url":"https://github.com/mmislan/palomar-quantitative-permanence/tree/e542422946035f4509e92c963b494e586105d09d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-11-000020-v1.json","repo":"https://github.com/mmislan/palomar-quantitative-permanence","tags":["math.DS","q-bio.MN","msc:37N25","msc:92C42","mass-action-kinetics","reaction-networks","dynamical-systems"],"score":0,"title":"Quantitative permanence and recovery with vanishing reverse rates","trust":"high","domain":"math.DS","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.DS","summary":"Quantitative permanence and recovery bounds are established for mass-action systems with vanishing reverse rates. For a finite weakly reversible network with rates proportional to powers of epsilon, eventual concentration bounds depend on the spread of the rate exponents, with geometric constants chosen before the individual rates. For an explicit three-species network, a prepared region admits global positive solutions with three distinct concentration scales. Every prepared solution reaches and remains in a smaller target by time (31/10)/(p^2 h^7), while an explicit prepared solution…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-11","reactions":{},"formalized":true,"formalizes":[{"title":"Quantitative permanence and recovery with vanishing reverse rates","identifier":"","relationship":"formalizes"},{"title":"Uniform permanence in weakly reversible mass-action systems","identifier":"","relationship":"adapts"},{"title":"Boundedness and persistence of weakly reversible mass-action systems","identifier":"","relationship":"adapts"}]}