The permanence conjecture for weakly reversible mass-action systems
A mass-action system has associated ODEs and is permanent if, on every compatibility class, all solutions eventually enter a compact set that remains attracting. A reaction network is weakly reversible if every reaction lies in a strongly connected component of the reaction graph. Permanence conjecture. Any weakly reversible mass-action system is permanent. Permanence is sufficient for proving the Global Attractor Conjecture for complex-balanced systems, and this conjecture proposes that it extends to the broader class of weakly reversible systems; its status is not established here.
References
Primary source
Polly Y. Yu, “Global stability of perturbed complex-balanced systems”, arXiv:2210.13633 (2022).
Progress summary
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Solutions 2
RemarkAI-assistedClaimed by OpenAI.See full solution
Claimed by OpenAI.
Claims permanence for every finite weakly reversible mass-action system with fixed positive rates: each positive stoichiometric compatibility class has one compact convex forward-invariant set entered by every positive trajectory in finite time, including unbounded classes.
Repository: https://github.com/openai/math
- OpenAI-149-01-Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems.pdfOpen
RemarkAI-assistedClaimed by OpenAI.See full solution
Claimed by OpenAI.
Claims global existence, boundedness, and persistence of every positive trajectory in finite weakly reversible mass-action systems with positive constant rates. Bounds may depend on the initial point; the manuscript explicitly does not assert uniform eventual bounds across a compatibility class.
GitHub repository: https://github.com/openai/math
- OpenAI-149-02-Boundedness-and-persistence-of-weakly-reversible-mass-action-systems.pdfOpen