Butterfly effect (English Wikipedia)

Rudnick, Ze'ev (January 2008). "What is... Quantum Chaos?" (PDF). Notices of the American Mathematical Society. Archived (PDF) from the original on 2009-10-02.

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arxiv.org (Global: 49^th place; English: 31^st place)

Motter, Adilson E.; Campbell, David K. (2013). "Chaos at fifty". Physics Today. 66 (5): 27–33. arXiv:1306.5777. Bibcode:2013PhT....66e..27M. doi:10.1063/PT.3.1977. S2CID 54005470.
Yan, Bin; Sinitsyn, Nikolai A. (2020). "Recovery of Damaged Information and the Out-of-Time-Ordered Correlators". Physical Review Letters. 125 (4) 040605. arXiv:2003.07267. Bibcode:2020PhRvL.125d0605Y. doi:10.1103/PhysRevLett.125.040605. PMID 32794812. S2CID 212725801.
Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H. (2002). "Quantum Chaotic Environments, the Butterfly Effect, and Decoherence". Physical Review Letters. 89 (17) 170405. arXiv:quant-ph/0111002. Bibcode:2002PhRvL..89q0405K. doi:10.1103/PhysRevLett.89.170405. PMID 12398653. S2CID 33363344.
Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond & Ollivier, Harold (2004). "Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay". Physical Review Letters. 92 (17) 177906. arXiv:quant-ph/0310038. Bibcode:2004PhRvL..92q7906P. doi:10.1103/PhysRevLett.92.177906. PMID 15169196. S2CID 6218604.

bbvaopenmind.com (Global: low place; English: low place)

"When Lorenz Discovered the Butterfly Effect". 22 May 2015. Retrieved 23 December 2021.

books.google.com (Global: 3^rd place; English: 3^rd place)

Steves, Bonnie; Maciejewski, AJ (September 2001). The Restless Universe Applications of Gravitational N-Body Dynamics to Planetary Stellar and Galactic Systems. USA: CRC Press. ISBN 0-7503-0822-2. Retrieved January 6, 2014.

copernicus.org (Global: 5,068^th place; English: 3,578^th place)

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Shen, Bo-Wen; Pielke Sr., Roger; Zeng, Xubin (2024-07-24). "Revisiting Lorenz's and Lilly's Empirical Formulas for Predictability Estimates". EGUsphere: 1–0. doi:10.13140/RG.2.2.32941.15849.

creativecommons.org (Global: 580^th place; English: 287^th place)

Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Zeng, Xiping (2023-07-22). "Lorenz's View on the Predictability Limit of the Atmosphere". Encyclopedia. 3 (3): 887–899. doi:10.3390/encyclopedia3030063. ISSN 2673-8392. This article incorporates text from this source, which is available under the CC BY 4.0 license.

doi.org (Global: 2^nd place; English: 2^nd place)

Lorenz, Edward N. (March 1963). "Deterministic Nonperiodic Flow". Journal of the Atmospheric Sciences. 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:dnf>2.0.co;2.
Rouvas-Nicolis, Catherine; Nicolis, Gregoire (4 May 2009). "Butterfly effect". Scholarpedia. Vol. 4. p. 1720. Bibcode:2009SchpJ...4.1720R. doi:10.4249/scholarpedia.1720. Archived from the original on 2016-01-02. Retrieved 2016-01-02.
Motter, Adilson E.; Campbell, David K. (2013). "Chaos at fifty". Physics Today. 66 (5): 27–33. arXiv:1306.5777. Bibcode:2013PhT....66e..27M. doi:10.1063/PT.3.1977. S2CID 54005470.
Lorenz, Edward N. (1963). "The Predictability of Hydrodynamic Flow" (PDF). Transactions of the New York Academy of Sciences. 25 (4): 409–432. doi:10.1111/j.2164-0947.1963.tb01464.x. Archived (PDF) from the original on 10 October 2014. Retrieved 1 September 2014.
Orrell, David; Smith, Leonard; Barkmeijer, Jan; Palmer, Tim (2001). "Model error in weather forecasting". Nonlinear Processes in Geophysics. 9 (6): 357–371. Bibcode:2001NPGeo...8..357O. doi:10.5194/npg-8-357-2001.
Orrell, David (2002). "Role of the metric in forecast error growth: How chaotic is the weather?". Tellus. 54A (4): 350–362. Bibcode:2002TellA..54..350O. doi:10.3402/tellusa.v54i4.12159.
Shen, Bo-Wen (2019). "Aggregated Negative Feedback in a Generalized Lorenz Model". International Journal of Bifurcation and Chaos. 29 (3): 1950037–1950091. Bibcode:2019IJBC...2950037S. doi:10.1142/S0218127419500378. S2CID 132494234.
Lorenz, Edward N. (June 1969). "The predictability of a flow which possesses many scales of motion". Tellus. XXI (3): 289–297. Bibcode:1969Tell...21..289L. doi:10.3402/tellusa.v21i3.10086.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin (2022-05-07). "One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models". Atmosphere. 13 (5): 753. Bibcode:2022Atmos..13..753S. doi:10.3390/atmos13050753. ISSN 2073-4433.
Shen, Bo-Wen (2014-05-01). "Nonlinear Feedback in a Five-Dimensional Lorenz Model". Journal of the Atmospheric Sciences. 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. doi:10.1175/JAS-D-13-0223.1. ISSN 0022-4928. S2CID 123683839.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Cui, Jialin; Faghih-Naini, Sara; Paxson, Wei; Atlas, Robert (2022-07-04). "Three Kinds of Butterfly Effects within Lorenz Models". Encyclopedia. 2 (3): 1250–1259. doi:10.3390/encyclopedia2030084. ISSN 2673-8392.
Shen, Bo-Wen; Pielke Sr., Roger; Zeng, Xubin (2024-07-24). "Revisiting Lorenz's and Lilly's Empirical Formulas for Predictability Estimates". EGUsphere: 1–0. doi:10.13140/RG.2.2.32941.15849.
Saiki, Yoshitaka; Yorke, James A. (2023-05-02). "Can the Flap of a Butterfly's Wings Shift a Tornado into Texas—Without Chaos?". Atmosphere. 14 (5): 821. Bibcode:2023Atmos..14..821S. doi:10.3390/atmos14050821. ISSN 2073-4433.
Pielke Sr., Roger; Shen, Bo-Wen; Zeng, Xubin (2024-05-01). "The Butterfly Effect: Can a butterfly in Brazil cause a tornado in Texas?". Weatherwise. 77 (3): 14–18. doi:10.1080/00431672.2024.2329521.
Palmer, Tim (2024-05-01). "The real butterfly effect and maggoty apples". Physics Today. 77 (5): 30–35. Bibcode:2024PhT....77e..30P. doi:10.1063/pt.eike.hsbz. ISSN 0031-9228.
Pielke, Roger A.; Shen, Bo-Wen; Zeng, Xubin (2024-09-01). "Butterfly effects". Physics Today. 77 (9): 10. Bibcode:2024PhT....77Q..10P. doi:10.1063/pt.ifge.djjy. ISSN 0031-9228.
Palmer, Tim (2024-09-01). "Butterfly effects". Physics Today. 77 (9): 10. Bibcode:2024PhT....77R..10P. doi:10.1063/pt.oktn.zdwa. ISSN 0031-9228. Archived from the original on 2024-11-23. Retrieved 2024-09-05.
Shen, Bo-Wen; Pielke, Roger; Xubin Zeng (2024-09-02). "Summary of Two Kinds of Butterfly Effects". Technical Report. doi:10.13140/RG.2.2.32401.24163.
Lighthill, James (1986-09-08). "The recently recognized failure of predictability in Newtonian dynamics". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 407 (1832): 35–50. Bibcode:1986RSPSA.407...35L. doi:10.1098/rspa.1986.0082. ISSN 0080-4630. S2CID 86552243.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Zeng, Xiping (2023-07-22). "Lorenz's View on the Predictability Limit of the Atmosphere". Encyclopedia. 3 (3): 887–899. doi:10.3390/encyclopedia3030063. ISSN 2673-8392. This article incorporates text from this source, which is available under the CC BY 4.0 license.
National Research Council (1966-01-01). The Feasibility of a Global Observation and Analysis Experiment. Bibcode:1966nap..book21272N. doi:10.17226/21272. ISBN 978-0-309-35922-1.
GARP (1969-03-01). "A Guide to GARP". Bull. Amer. Meteor. Soc. 50 (3): 136–141. Bibcode:1969BAMS...50..136.. doi:10.1175/1520-0477-50.3.136.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Zeng, Xiping (2024-07-16). "Exploring the Origin of the Two-Week Predictability Limit: A Revisit of Lorenz's Predictability Studies in the 1960s". Atmosphere. 15 (7): 837. Bibcode:2024Atmos..15..837S. doi:10.3390/atmos15070837. ISSN 2073-4433.
Heller, E. J.; Tomsovic, S. (July 1993). "Postmodern Quantum Mechanics". Physics Today. 46 (7): 38–46. Bibcode:1993PhT....46g..38H. doi:10.1063/1.881358.
Berry, Michael (1989). "Quantum chaology, not quantum chaos". Physica Scripta. 40 (3): 335–336. Bibcode:1989PhyS...40..335B. doi:10.1088/0031-8949/40/3/013. S2CID 250776260.
Gutzwiller, Martin C. (1971). "Periodic Orbits and Classical Quantization Conditions". Journal of Mathematical Physics. 12 (3): 343. Bibcode:1971JMP....12..343G. doi:10.1063/1.1665596.
Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas". Physical Review A. 46 (3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. S2CID 7877923. Archived from the original on 2024-02-03. Retrieved 2021-11-27.
Yan, Bin; Sinitsyn, Nikolai A. (2020). "Recovery of Damaged Information and the Out-of-Time-Ordered Correlators". Physical Review Letters. 125 (4) 040605. arXiv:2003.07267. Bibcode:2020PhRvL.125d0605Y. doi:10.1103/PhysRevLett.125.040605. PMID 32794812. S2CID 212725801.
Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H. (2002). "Quantum Chaotic Environments, the Butterfly Effect, and Decoherence". Physical Review Letters. 89 (17) 170405. arXiv:quant-ph/0111002. Bibcode:2002PhRvL..89q0405K. doi:10.1103/PhysRevLett.89.170405. PMID 12398653. S2CID 33363344.
Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond & Ollivier, Harold (2004). "Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay". Physical Review Letters. 92 (17) 177906. arXiv:quant-ph/0310038. Bibcode:2004PhRvL..92q7906P. doi:10.1103/PhysRevLett.92.177906. PMID 15169196. S2CID 6218604.
Lee, Jae-Seung & Khitrin, A. K. (2004). "Quantum amplifier: Measurement with entangled spins". Journal of Chemical Physics. 121 (9): 3949–51. Bibcode:2004JChPh.121.3949L. doi:10.1063/1.1788661. PMID 15332940.

encyclopedia.pub (Global: low place; English: low place)

Shen, Bo-Wen; Pielke, Sr., Roger; Zeng, Xubin; Zeng, Xiping (2023-09-13). "Lorenz's View on the Predictability Limit". Encyclopedia pub. Archived from the original on 2025-03-19. Retrieved 2023-09-13.

ghostarchive.org (Global: 64^th place; English: 28^th place)

"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" (PDF). Archived (PDF) from the original on 2022-10-09. Retrieved 23 December 2021.
Tim, Palmer (19 May 2017). "The Butterfly Effect – What Does It Really Signify?". Oxford U. Dept. of Mathematics Youtube Channel. Archived from the original on 2021-10-31. Retrieved 13 February 2019.
Emanuel, Kerry (26 March 2018). "Edward N. Lorenz and the End of the Cartesian Universe". MIT Department of Earth, Atmospheric, and Planetary Sciences Youtube channel. Archived from the original on 2021-10-31. Retrieved 13 February 2019.

inquirer.com (Global: 1,419^th place; English: 693^rd place)

Flam, Faye (2012-06-15). "The Physics of Ray Bradbury's "A Sound of Thunder"". The Philadelphia Inquirer. Archived from the original on 2015-09-24. Retrieved 2015-09-02.

iqc.ca (Global: low place; English: low place)

Poulin, David. "A Rough Guide to Quantum Chaos" (PDF). Archived from the original (PDF) on 2010-11-04.

mathsciencehistory.com (Global: low place; English: low place)

"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?" (PDF). Archived (PDF) from the original on 2022-10-09. Retrieved 23 December 2021.

mit.edu (Global: 476^th place; English: 340^th place)

eapsweb.mit.edu

Lorenz, Edward N. (1963). "The Predictability of Hydrodynamic Flow" (PDF). Transactions of the New York Academy of Sciences. 25 (4): 409–432. doi:10.1111/j.2164-0947.1963.tb01464.x. Archived (PDF) from the original on 10 October 2014. Retrieved 1 September 2014.

nih.gov (Global: 5^th place; English: 5^th place)

pubmed.ncbi.nlm.nih.gov

Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas". Physical Review A. 46 (3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. S2CID 7877923. Archived from the original on 2024-02-03. Retrieved 2021-11-27.
Yan, Bin; Sinitsyn, Nikolai A. (2020). "Recovery of Damaged Information and the Out-of-Time-Ordered Correlators". Physical Review Letters. 125 (4) 040605. arXiv:2003.07267. Bibcode:2020PhRvL.125d0605Y. doi:10.1103/PhysRevLett.125.040605. PMID 32794812. S2CID 212725801.
Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H. (2002). "Quantum Chaotic Environments, the Butterfly Effect, and Decoherence". Physical Review Letters. 89 (17) 170405. arXiv:quant-ph/0111002. Bibcode:2002PhRvL..89q0405K. doi:10.1103/PhysRevLett.89.170405. PMID 12398653. S2CID 33363344.
Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond & Ollivier, Harold (2004). "Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay". Physical Review Letters. 92 (17) 177906. arXiv:quant-ph/0310038. Bibcode:2004PhRvL..92q7906P. doi:10.1103/PhysRevLett.92.177906. PMID 15169196. S2CID 6218604.
Lee, Jae-Seung & Khitrin, A. K. (2004). "Quantum amplifier: Measurement with entangled spins". Journal of Chemical Physics. 121 (9): 3949–51. Bibcode:2004JChPh.121.3949L. doi:10.1063/1.1788661. PMID 15332940.

oup.com (Global: 292^nd place; English: 233^rd place)

academic.oup.com

"Computing Machinery and Intelligence". Archived from the original on 2020-09-08. Retrieved 2022-08-16.

realclimate.org (Global: low place; English: low place)

"Chaos and Climate". RealClimate. 4 November 2005. Archived from the original on 2014-07-02. Retrieved 2014-06-08.

rgdoi.net (Global: low place; English: low place)

Shen, Bo-Wen; Pielke, Roger; Xubin Zeng (2024-09-02). "Summary of Two Kinds of Butterfly Effects". Technical Report. doi:10.13140/RG.2.2.32401.24163.

scholar.google.com (Global: 1,418^th place; English: 768^th place)

"Google Scholar citation record". Archived from the original on 2017-02-24. Retrieved 2015-05-23.

scholarpedia.org (Global: low place; English: low place)

Rouvas-Nicolis, Catherine; Nicolis, Gregoire (4 May 2009). "Butterfly effect". Scholarpedia. Vol. 4. p. 1720. Bibcode:2009SchpJ...4.1720R. doi:10.4249/scholarpedia.1720. Archived from the original on 2016-01-02. Retrieved 2016-01-02.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Motter, Adilson E.; Campbell, David K. (2013). "Chaos at fifty". Physics Today. 66 (5): 27–33. arXiv:1306.5777. Bibcode:2013PhT....66e..27M. doi:10.1063/PT.3.1977. S2CID 54005470.
Shen, Bo-Wen (2019). "Aggregated Negative Feedback in a Generalized Lorenz Model". International Journal of Bifurcation and Chaos. 29 (3): 1950037–1950091. Bibcode:2019IJBC...2950037S. doi:10.1142/S0218127419500378. S2CID 132494234.
Shen, Bo-Wen (2014-05-01). "Nonlinear Feedback in a Five-Dimensional Lorenz Model". Journal of the Atmospheric Sciences. 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. doi:10.1175/JAS-D-13-0223.1. ISSN 0022-4928. S2CID 123683839.
Lighthill, James (1986-09-08). "The recently recognized failure of predictability in Newtonian dynamics". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 407 (1832): 35–50. Bibcode:1986RSPSA.407...35L. doi:10.1098/rspa.1986.0082. ISSN 0080-4630. S2CID 86552243.
Berry, Michael (1989). "Quantum chaology, not quantum chaos". Physica Scripta. 40 (3): 335–336. Bibcode:1989PhyS...40..335B. doi:10.1088/0031-8949/40/3/013. S2CID 250776260.
Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas". Physical Review A. 46 (3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. S2CID 7877923. Archived from the original on 2024-02-03. Retrieved 2021-11-27.
Yan, Bin; Sinitsyn, Nikolai A. (2020). "Recovery of Damaged Information and the Out-of-Time-Ordered Correlators". Physical Review Letters. 125 (4) 040605. arXiv:2003.07267. Bibcode:2020PhRvL.125d0605Y. doi:10.1103/PhysRevLett.125.040605. PMID 32794812. S2CID 212725801.
Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H. (2002). "Quantum Chaotic Environments, the Butterfly Effect, and Decoherence". Physical Review Letters. 89 (17) 170405. arXiv:quant-ph/0111002. Bibcode:2002PhRvL..89q0405K. doi:10.1103/PhysRevLett.89.170405. PMID 12398653. S2CID 33363344.
Poulin, David; Blume-Kohout, Robin; Laflamme, Raymond & Ollivier, Harold (2004). "Exponential Speedup with a Single Bit of Quantum Information: Measuring the Average Fidelity Decay". Physical Review Letters. 92 (17) 177906. arXiv:quant-ph/0310038. Bibcode:2004PhRvL..92q7906P. doi:10.1103/PhysRevLett.92.177906. PMID 15169196. S2CID 6218604.

ualberta.ca (Global: 3,255^th place; English: 2,085^th place)

cs.ualberta.ca

"Part19". Cs.ualberta.ca. 1960-11-22. Archived from the original on 2009-07-17. Retrieved 2014-06-08.

web.archive.org (Global: 1^st place; English: 1^st place)

Rouvas-Nicolis, Catherine; Nicolis, Gregoire (4 May 2009). "Butterfly effect". Scholarpedia. Vol. 4. p. 1720. Bibcode:2009SchpJ...4.1720R. doi:10.4249/scholarpedia.1720. Archived from the original on 2016-01-02. Retrieved 2016-01-02.
Some Historical Notes: History of Chaos Theory Archived 2006-07-19 at the Wayback Machine
"Computing Machinery and Intelligence". Archived from the original on 2020-09-08. Retrieved 2022-08-16.
Flam, Faye (2012-06-15). "The Physics of Ray Bradbury's "A Sound of Thunder"". The Philadelphia Inquirer. Archived from the original on 2015-09-24. Retrieved 2015-09-02.
"Google Scholar citation record". Archived from the original on 2017-02-24. Retrieved 2015-05-23.
"Part19". Cs.ualberta.ca. 1960-11-22. Archived from the original on 2009-07-17. Retrieved 2014-06-08.
Lorenz, Edward N. (1963). "The Predictability of Hydrodynamic Flow" (PDF). Transactions of the New York Academy of Sciences. 25 (4): 409–432. doi:10.1111/j.2164-0947.1963.tb01464.x. Archived (PDF) from the original on 10 October 2014. Retrieved 1 September 2014.
"The Butterfly Effects: Variations on a Meme". AP42 ...and everything. Archived from the original on 11 November 2011. Retrieved 3 August 2011.
"Chaos and Climate". RealClimate. 4 November 2005. Archived from the original on 2014-07-02. Retrieved 2014-06-08.
Palmer, Tim (2024-09-01). "Butterfly effects". Physics Today. 77 (9): 10. Bibcode:2024PhT....77R..10P. doi:10.1063/pt.oktn.zdwa. ISSN 0031-9228. Archived from the original on 2024-11-23. Retrieved 2024-09-05.
Shen, Bo-Wen; Pielke, Sr., Roger; Zeng, Xubin; Zeng, Xiping (2023-09-13). "Lorenz's View on the Predictability Limit". Encyclopedia pub. Archived from the original on 2025-03-19. Retrieved 2023-09-13.
Rudnick, Ze'ev (January 2008). "What is... Quantum Chaos?" (PDF). Notices of the American Mathematical Society. Archived (PDF) from the original on 2009-10-02.
Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas". Physical Review A. 46 (3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. S2CID 7877923. Archived from the original on 2024-02-03. Retrieved 2021-11-27.
Poulin, David. "A Rough Guide to Quantum Chaos" (PDF). Archived from the original (PDF) on 2010-11-04.

wm.edu (Global: 4,824^th place; English: 2,652^nd place)

scholarworks.wm.edu

Gao, J. & Delos, J. B. (1992). "Closed-orbit theory of oscillations in atomic photoabsorption cross sections in a strong electric field. II. Derivation of formulas". Physical Review A. 46 (3): 1455–1467. Bibcode:1992PhRvA..46.1455G. doi:10.1103/PhysRevA.46.1455. PMID 9908268. S2CID 7877923. Archived from the original on 2024-02-03. Retrieved 2021-11-27.

wolframscience.com (Global: low place; English: low place)

Some Historical Notes: History of Chaos Theory Archived 2006-07-19 at the Wayback Machine

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Lorenz, Edward N. (1993). The essence of chaos. London: UCL Press. ISBN 0-203-21458-7. OCLC 56620850.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin (2022-05-07). "One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models". Atmosphere. 13 (5): 753. Bibcode:2022Atmos..13..753S. doi:10.3390/atmos13050753. ISSN 2073-4433.
W., Jordan, Dominic (2011). Nonlinear ordinary differential equations: an introduction for scientists and engineers. Oxford Univ. Press. ISBN 978-0-19-920825-8. OCLC 772641393.{{cite book}}: CS1 maint: multiple names: authors list (link)
Shen, Bo-Wen (2014-05-01). "Nonlinear Feedback in a Five-Dimensional Lorenz Model". Journal of the Atmospheric Sciences. 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. doi:10.1175/JAS-D-13-0223.1. ISSN 0022-4928. S2CID 123683839.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Cui, Jialin; Faghih-Naini, Sara; Paxson, Wei; Atlas, Robert (2022-07-04). "Three Kinds of Butterfly Effects within Lorenz Models". Encyclopedia. 2 (3): 1250–1259. doi:10.3390/encyclopedia2030084. ISSN 2673-8392.
Saiki, Yoshitaka; Yorke, James A. (2023-05-02). "Can the Flap of a Butterfly's Wings Shift a Tornado into Texas—Without Chaos?". Atmosphere. 14 (5): 821. Bibcode:2023Atmos..14..821S. doi:10.3390/atmos14050821. ISSN 2073-4433.
Palmer, Tim (2024-05-01). "The real butterfly effect and maggoty apples". Physics Today. 77 (5): 30–35. Bibcode:2024PhT....77e..30P. doi:10.1063/pt.eike.hsbz. ISSN 0031-9228.
Pielke, Roger A.; Shen, Bo-Wen; Zeng, Xubin (2024-09-01). "Butterfly effects". Physics Today. 77 (9): 10. Bibcode:2024PhT....77Q..10P. doi:10.1063/pt.ifge.djjy. ISSN 0031-9228.
Palmer, Tim (2024-09-01). "Butterfly effects". Physics Today. 77 (9): 10. Bibcode:2024PhT....77R..10P. doi:10.1063/pt.oktn.zdwa. ISSN 0031-9228. Archived from the original on 2024-11-23. Retrieved 2024-09-05.
Lighthill, James (1986-09-08). "The recently recognized failure of predictability in Newtonian dynamics". Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 407 (1832): 35–50. Bibcode:1986RSPSA.407...35L. doi:10.1098/rspa.1986.0082. ISSN 0080-4630. S2CID 86552243.
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