Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations—A model for catalytic hypercycles
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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 [56]
Cites
Selforganization of matter and the evolution of biological macromolecules
Eigen, M. (1971) · Die Naturwissenschaften · doi:10.1007/bf00623322 · Cited by 3,788 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Competition and cooperation in catalytic selfreplication
Hofbauer, J., Schuster, P., & Sigmund, K. (1981) · Journal of Mathematical Biology · doi:10.1007/bf00275439 · Cited by 50 · see citing works
Self-citationEcology 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
The influence of mutation on autocatalytic reaction networks
Stadler, P. F., & Nuño, J. C. (1994) · Mathematical Biosciences · doi:10.1016/0025-5564(94)90055-8 · Cited by 12 · see citing works
- Authors
- SCHUSTER, P., SIGMUND, K., & WOLFF, R.
- Affiliations
- University of Vienna (AT)
- Venue
- Bulletin of Mathematical Biology
- Published
- 1978
- Volume
- 40
- Issue
- 6
- Pages
- 743-769
- ISSN
- 0092-8240 (ISSN-L)
- OpenAlex
- W2019095004
- Cited by
- 58
- References
- 1
- Citations by year
- 2026: 1 · 2022: 2 · 2021: 1 · 2020: 1 · 2019: 1 · 2018: 3 · 2017: 1 · 2016: 3 · 2015: 1 · 2012: 1
- FWCI
- 8.83
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Bulletin of Mathematical Biology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Keywords
- nonlinear differential equations, topological analysis, dynamical systems, autocatalytic sets, chemical reaction networks
- MeSH terms
- Catalysis, Mathematics, Models, Biological, Models, Chemical, Periodicity, Macromolecular Substances
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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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