Time-averaged observables exhibit kink or higher-order derivative singularities at supercritical Hopf bifurcations because phase averaging eliminates odd powers of the limit-cycle amplitude while the squared amplitude varies smoothly.
Schnakenberg, Simple chemical reaction systems with limit cycle behaviour, J
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Open CRN behavior and thermodynamics, including local detailed balance and entropy production, emerge to leading order from closed CRNs via time-scale and abundance separations for arbitrary stoichiometries.
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Singular Behavior of Observables at Hopf Bifurcations
Time-averaged observables exhibit kink or higher-order derivative singularities at supercritical Hopf bifurcations because phase averaging eliminates odd powers of the limit-cycle amplitude while the squared amplitude varies smoothly.
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Emergence of Open Chemical Reaction Network Thermodynamics within Closed Systems
Open CRN behavior and thermodynamics, including local detailed balance and entropy production, emerge to leading order from closed CRNs via time-scale and abundance separations for arbitrary stoichiometries.