The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
An extremum principle for parabolic competition
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Varga and Szathmáry showed that there is a single internal and globally stable rest point of the system of Equation (11).
“This result was extended by Varga and Szathmáry [78] showing that there is a single internal and globally stable rest point of the system of Equation (11).”
From Ecology and Evolution in the RNA World Dynamics and Stability of Prebiotic Replicator Systems (2017) · cites this paper as [78]
Citations
Cites
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Research works printed but not linked: 1
- Szathmáry, E. 1989. The emergence, maintenance, and transitions of the earliest evolutionary units.Oxf. Surv. Evol. Biol. 6, 169–205.
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The origin of replicators and reproducers
Szathmáry, E. (2006) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2006.1912 · Cited by 200
Self-citationDiversity begets stability: Sublinear growth and competitive coexistence across ecosystems
Hatton, I. A., Mazzarisi, O., Altieri, A., & Smerlak, M. (2024) · Science · doi:10.1126/science.adg8488 · Cited by 176
The dynamics of the RNA world: insights and challenges
Kun, Á., Szilágyi, A., Könnyű, B., Boza, G., Zachar, I., & Szathmáry, E. (2015) · Annals of the New York Academy of Sciences · doi:10.1111/nyas.12700 · Cited by 65
Self-citationSelection dynamics in autocatalytic systems: Templates replicating through binary ligation
Wills, P. R. (1998) · Bulletin of Mathematical Biology · doi:10.1016/s0092-8240(98)90003-9 · Cited by 65
Survival of Replicators with Parabolic Growth Tendency and Exponential Decay
SCHEURING, I., & SZATHMÁRY, E. (2001) · Journal of Theoretical Biology · doi:10.1006/jtbi.2001.2360 · Cited by 48
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
Nature and evolution of early replicons
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Selection versus Coexistence of Parabolic Replicators Spreading on Surfaces
von Kiedrowski, G., & Szathmáry, E. (2001) · Selection · doi:10.1556/select.1.2000.1-3.17 · Cited by 30
Self-citationEmergence of protocellular growth laws
Rocheleau, T., Rasmussen, S., Nielsen, P. E., Jacobi, M. N., & Ziock, H. J. (2007) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2007.2076 · Cited by 25
Schuster, P. M., & Stadler, P. F. (2008) · Elsevier eBooks · doi:10.1016/b978-0-12-374153-0.00001-1 · Cited by 16
Adaptive Dynamics of Parabolic Replicators
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Self-citationEvolution of RNA-Based Networks
Stadler, P. F. (2015) · Current topics in microbiology and immunology · doi:10.1007/82_2015_470 · Cited by 11
Avoidance of error catastrophe via proofreading innate to template-directed polymerization
Matsubara, Y. J., Takeuchi, N., & Kaneko, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013170 · Cited by 8
Darwinian Aspects of Molecular Evolution at Sublinear Propagation Rates
Davis, B. (2000) · Bulletin of Mathematical Biology · doi:10.1006/bulm.2000.0173 · Cited by 6
Parabolic replicator dynamics and the principle of minimum Tsallis information gain
Karev, G. P., & Koonin, E. V. (2013) · Biology Direct · doi:10.1186/1745-6150-8-19 · Cited by 6
Paczkó, M., Szathmáry, E., & Szilágyi, A. (2024) · eLife · doi:10.7554/elife.93208 · Cited by 3
Self-citationExtended Discrete-Time Population Model to Describe the Competition of Nutrient-Producing Protocells
Kicsiny, R., Bódai, T., Székely, L., & Varga, Z. (2025) · Bulletin of Mathematical Biology · doi:10.1007/s11538-025-01488-0 · Cited by 2
Self-citationReplicator Dynamics in Protocells
Stadler, P. F., & Stadler, B. M. R. (2008) · The MIT Press eBooks · doi:10.7551/mitpress/9780262182683.003.0014 · Cited by 1
ON PERSISTENCE AND STABILITY OF COUPLED MAP LATTICES
Ahmed, E., & Hegazi, A. S. (2001) · Advances in Complex Systems · doi:10.1142/s0219525901000176
Subexponential replicator dynamics and the principle of minimal Tsallis information gain
Kareva, I., & Karev, G. P. (2019) · Elsevier eBooks · doi:10.1016/b978-0-12-814368-1.00009-6
Error Catastrophe Is Avoided by Proofreading Innate to Template-Directed PolymerizationPreprint
Matsubara, Y. J., Takeuchi, N., & Kaneko, K. (2021) · arXiv (Cornell University)
(2019) · Elsevier eBooks · doi:10.1016/b978-0-12-814368-1.09992-6
Paczkó, M., Szathmáry, E., & Szilágyi, A. (2024) · eLife · doi:10.7554/elife.93208.1
Self-citation
Metadata
- Authors
- Varga, Z., & Szathmáry, E.
- Affiliations
- Magyar Agrár- és Élettudományi Egyetem (HU)
- Eötvös Loránd University (HU)
- Corresponding author
- Szathmáry, Eörs
- ORCID
- Szathmáry, Eörs
- Venue
- Bulletin of Mathematical Biology
- Published
- 1997-11
- Volume
- 59
- Issue
- 6
- Pages
- 1145-1154
- ISSN
- 0092-8240 (ISSN-L)
- 1522-9602
- OpenAlex
- W4244405037
- Cited by
- 27
- References
- 9
- Citations by year
- 2025: 1 · 2024: 5 · 2023: 2 · 2021: 1 · 2019: 2 · 2017: 1 · 2015: 2 · 2013: 1
- FWCI
- 1.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Bulletin of Mathematical Biology (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical and Theoretical Epidemiology and Ecology Models
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Keywords
- parabolic growth, competition (biology), extremum principle, Lyapunov function, asymptotic stability, equilibrium, simplex, fractional order kinetics, population dynamics
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