A new Perron-Volterra Lyapunov construction unifies stability proofs for rank-one epidemic models and establishes the competitive exclusion partition property for two-strain cases.
DOI 10.48550/arXiv.2508.15273, 2508.15273
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The paper gives a chemical reaction network flavored generalization of the Next Generation Matrix theorem and reviews a symbolic-numeric approach for bifurcation analysis in positive ODEs using child selection minors.
Stoichiometric models of the Notch-Delta pathway identify symmetry-induced bifurcations and key structural features that enable neighboring cells to adopt different fates without assuming particular kinetics.
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From the Volterra type Lyapunov functions of Rahman-Zou towards a competitive exclusion partition property for rank one models
A new Perron-Volterra Lyapunov construction unifies stability proofs for rank-one epidemic models and establishes the competitive exclusion partition property for two-strain cases.
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Enumeration of Autocatalytic Subsystems in Large Chemical Reaction Networks
An efficient enumeration algorithm is developed from sufficient conditions on subgraphs in the bipartite König representation to identify autocatalytic subnetworks and minimal cores in full metabolic networks.
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Emergent conserved quantities via irreversibility
Irreversible reactions generate emergent conservation laws and broken cycles in CRNs and Markov chains via a co-production index, extending the index law and resolving non-integer conservation conundrums.
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A cocktail of chemical reaction networks and mathematical epidemiology tools for positive ODE stability problems
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Mathematical modeling and analysis of the Notch-Delta pathway
Stoichiometric models of the Notch-Delta pathway identify symmetry-induced bifurcations and key structural features that enable neighboring cells to adopt different fates without assuming particular kinetics.