Competitive Exclusion of Disjoint Hypercycles
Abstract
A conjecture of Eigen and Schuster (1979) concerning the competitive exclusion of disjoint hypercycles is finally proved.
Integrity 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?
Even if starting from same concentration, no coexistence of competing hypercycles is possible.
“Even if we start from the same concentration, no coexistence of competing hypercycles is possible [68].”
From Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems (2017) · cites this paper as [68]
Cites
The Hypercycle: A principle of natural self-organization
Eigen, M., & Schuster, P. M. (1979) · Cited by 1,906 · see citing works
The theory of evolution and dynamical systems
Hofbauer, J. (1988) · Cited by 1,295 · see citing works
Self-citationSchuster, P., Sigmund, K., & Wolff, R. (1979) · Journal of Differential Equations · doi:10.1016/0022-0396(79)90039-1 · Cited by 129 · see citing works
Stable periodic solutions for the hypercycle system
Hofbauer, J., Mallet-Paret, J., & Smith, H. L. (1991) · Journal of Dynamics and Differential Equations · doi:10.1007/bf01049740 · Cited by 41 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Stadler, B. M. R., & Stadler, P. F. (2003) · Advances in Complex Systems · doi:10.1142/s0219525903000724 · Cited by 47 · see citing works
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
“Even if we start from the same concentration, no coexistence of competing hypercycles is possible [68].”
BackgroundOn the evolution of hypercycles
Bratus, A. S., Drozhzhin, S., & Yakushkina, T. (2018) · Mathematical Biosciences · doi:10.1016/j.mbs.2018.09.001 · Cited by 10 · see citing works
Stability and the limit behavior of the open distributed hypercycle system
Bratus, A. S., & Lukasheva, E. N. (2009) · Differential Equations · doi:10.1134/s0012266109110024 · Cited by 7 · see citing works
Autocatalytic Networks: An Intimate Relation between Network Topology and Dynamics
Joshi, B., & Crăciun, G. (2021) · SIAM Journal on Applied Mathematics · doi:10.1137/20m1342720 · Cited by 3 · see citing works
Fitness optimization and evolution of permanent replicator systems
Drozhzhin, S., Yakushkina, T., & Bratus, A. S. (2021) · Journal of Mathematical Biology · doi:10.1007/s00285-021-01548-8 · Cited by 2 · see citing works
Open quasispecies systems: New approach to evolutionary adaptation
Samokhin, I., Yakushkina, T., & Bratus, A. S. (2021) · Chinese Journal of Physics · doi:10.1016/j.cjph.2021.11.004 · Cited by 1 · see citing works
On a hypercycle equation with infinitely many members
Bratus, A. S., Chmereva, O. S., Yegorov, I., & Novozhilov, A. S. (2023) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2022.126988
- Authors
- Hofbauer, J.
- Affiliations
- University of Vienna (AT)
- Corresponding author
- Hofbauer, Josef
- Venue
- Zeitschrift für Physikalische Chemie
- Publisher
- Walter de Gruyter GmbH
- Published
- 2002-01-01
- Volume
- 216
- Issue
- 1
- ISSN
- 0044-3336 (ISSN-L)
- 2196-7156
- 0942-9352
- OpenAlex
- W2112901742
- Cited by
- 8
- References
- 4
- Citations by year
- 2023: 1 · 2021: 3 · 2018: 1 · 2017: 1
- FWCI
- 0.35
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Zeitschrift für Physikalische Chemie (publishedVersion)
- Topics
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Keywords
- competitive exclusion, autocatalytic sets, molecular evolution, replicator dynamics
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
