Dynamical systems under constant organization. III. Cooperative and competitive behavior of hypercycles
Open accessIntegrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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 [52]
Assuming all catalytic rates same, hypercycles with 2,3,4 members have stable fixed point; with 5 or more approach stable limit cycle.
“Assuming that all catalytic rates are the same, the dynamics leads to a stable fixed point for two-, three- and four-membered hypercycles [51,52]. Furthermore, if there are five or more members in the hypercycle, then the system approaches a stable limit cycle.”
From Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems (2017) · cites this paper as [52]
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
“Assuming that all catalytic rates are the same, the dynamics leads to a stable fixed point for two-, three- and four-membered hypercycles [51,52].”
BackgroundCompetitive Exclusion of Disjoint Hypercycles
Hofbauer, J. (2002) · Zeitschrift für Physikalische Chemie · doi:10.1524/zpch.2002.216.1.035 · Cited by 8 · see citing works
- Authors
- Schuster, P., Sigmund, K., & Wolff, R.
- Affiliations
- University of Vienna (AT)
- Venue
- Journal of Differential Equations
- Publisher
- Elsevier BV
- Published
- 1979-06
- Volume
- 32
- Issue
- 3
- Pages
- 357-368
- ISSN
- 0022-0396 (ISSN-L)
- OpenAlex
- W1986864321
- Cited by
- 129
- References
- 1
- Citations by year
- 2025: 2 · 2024: 2 · 2023: 1 · 2022: 4 · 2021: 2 · 2020: 3 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 2 · 2014: 5 · 2013: 5
- FWCI
- 13.17
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Differential Equations (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 › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Systems and Dynamics
- Keywords
- hypercycles, cooperative behavior, competitive behavior, molecular self-organization, dynamical systems, qualitative analysis, differential equations
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
