A general cooperation theorem for hypercycles
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In inhomogeneous hypercycle (Ai>0), if Ai values too large compared to Ki, one or more sequences can be lost.
“In the inhomogeneous hypercycle (Ai > 0) the members are also in competition and if the Ai values are too large compared to the Ki values, then one or more of the sequences can be lost [54].”
From Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems (2017) · cites this paper as [54]
In homogeneous hypercycle (Ai=0), all members coexist.
“If for all i, Ai = 0, i.e., the replicators cannot replicate on their own, only with the help of another catalyst, then the system is fully cooperative and all members coexist [51,52,53,54,55,56].”
From Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems (2017) · cites this paper as [54]
Cited by
Sorted by citations
Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems
Szilágyi, A., Zachar, I., Scheuring, I., Kun, Á., Könnyű, B., & Czárán, T. (2017) · Life · doi:10.3390/life7040048 · Cited by 44 · see citing works
“In the inhomogeneous hypercycle (Ai > 0) the members are also in competition and if the Ai values are too large compared to the Ki values, then one or more of the sequences can be lost [54].”
BackgroundA Difference Equation Model for the Hypercycle
Hofbauer, J. (1984) · SIAM Journal on Applied Mathematics · doi:10.1137/0144054 · Cited by 22 · see citing works
Self-citation
- Authors
- Hofbauer, J.
- Affiliations
- University of Vienna (AT)
- Corresponding author
- Hofbauer, Josef
- Venue
- Monatshefte f�r Mathematik
- Published
- 1981-09
- Volume
- 91
- Issue
- 3
- Pages
- 233-240
- ISSN
- 0026-9255 (ISSN-L)
- 1436-5081
- OpenAlex
- W2005026976
- Cited by
- 160
- References
- 0
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 1 · 2023: 3 · 2022: 9 · 2021: 5 · 2020: 5 · 2019: 4 · 2018: 7 · 2017: 5 · 2016: 4 · 2014: 3 · 2013: 6
- FWCI
- 4.52
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Monatshefte für Mathematik (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Control and Stability of Dynamical Systems
- Keywords
- hypercycles, attractors, compact dynamical systems, Lyapunov function, time averages, cyclic symmetry
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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