混沌理论 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "混沌理论" in Chinese language version.

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journals.ametsoc.org

Shen, Bo-Wen. Nonlinear Feedback in a Five-Dimensional Lorenz Model. Journal of the Atmospheric Sciences. 2014-05-01, 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. ISSN 0022-4928. S2CID 123683839. doi:10.1175/JAS-D-13-0223.1 （英语）.

archive.org

Ivancevic, Vladimir G.; Tijana T. Ivancevic. Complex nonlinearity: chaos, phase transitions, topology change, and path integrals. Springer. 2008. ISBN 978-3-540-79356-4.
Poincaré, J. Henri. The three-body problem and the equations of dynamics : Poincaré's foundational work on dynamical systems theory. Popp, Bruce D. (Translator). Cham, Switzerland: Springer International Publishing. 2017. ISBN 9783319528984. OCLC 987302273.
Berger J.M.; Mandelbrot B. A new model for error clustering in telephone circuits. IBM Journal of Research and Development. 1963, 7 (3): 224–236. doi:10.1147/rd.73.0224.
See also: Mandelbrot, Benoît B.; Hudson, Richard L. The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books. 2004: 201. ISBN 9780465043552.
Mandelbrot, B. The Fractal Geometry of Nature. New York: Macmillan. 1982. ISBN 978-0716711865.
Gleick, James. Chaos: Making a New Science. Penguin Books. August 26, 2008. ISBN 978-0143113454.
Banks; Brooks; Cairns; Davis; Stacey. On Devaney's definition of chaos. The American Mathematical Monthly. 1992, 99 (4): 332–334. doi:10.1080/00029890.1992.11995856.
Vellekoop, Michel; Berglund, Raoul. On Intervals, Transitivity = Chaos. The American Mathematical Monthly. April 1994, 101 (4): 353–5. JSTOR 2975629. doi:10.2307/2975629.
Medio, Alfredo; Lines, Marji. Nonlinear Dynamics: A Primer. Cambridge University Press. 2001: 165. ISBN 978-0-521-55874-7.
Watts, Robert G. Global Warming and the Future of the Earth. Morgan & Claypool. 2007: 17.
Werndl, Charlotte. What are the New Implications of Chaos for Unpredictability?. The British Journal for the Philosophy of Science. 2009, 60 (1): 195–220. S2CID 354849. arXiv:1310.1576 . doi:10.1093/bjps/axn053.
Rosario, Pedro. Underdetermination of Science: Part I. Lulu.com. 2006. ISBN 978-1411693913. ^{[自述来源]}
Kyrtsou C.; Labys W. Evidence for chaotic dependence between US inflation and commodity prices. Journal of Macroeconomics. 2006, 28 (1): 256–266. doi:10.1016/j.jmacro.2005.10.019.
Kyrtsou, C.; M. Terraza. Is it possible to study chaotic and ARCH behaviour jointly? Application of a noisy Mackey-Glass equation with heteroskedastic errors to the Paris Stock Exchange returns series. Computational Economics. 2003, 21 (3): 257–276. S2CID 154202123. doi:10.1023/A:1023939610962.
Williams, Bill Williams, Justine. Trading chaos : maximize profits with proven technical techniques 2nd. New York: Wiley. 2004. ISBN 9780471463085.
Peters, Edgar E. Fractal market analysis : applying chaos theory to investment and economics 2. print. New York u.a.: Wiley. 1994. ISBN 978-0471585244.
Goswami, Ambarish; Thuilot, Benoit; Espiau, Bernard. A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos. The International Journal of Robotics Research. 1998, 17 (12): 1282–1301. CiteSeerX 10.1.1.17.4861 . S2CID 1283494. doi:10.1177/027836499801701202.

archive.today

Applying Chaos Theory to Embedded Applications. （原始内容存档于2011-08-09）.

arxiv.org

Motter, A. E.; Campbell, D. K. Chaos at fifty. Phys. Today. 2013, 66 (5): 27–33. Bibcode:2013PhT....66e..27M. S2CID 54005470. arXiv:1306.5777 . doi:10.1063/pt.3.1977.
Werndl, Charlotte. What are the New Implications of Chaos for Unpredictability?. The British Journal for the Philosophy of Science. 2009, 60 (1): 195–220. S2CID 354849. arXiv:1310.1576 . doi:10.1093/bjps/axn053.
Okulov, A Yu. Structured light entities, chaos and nonlocal maps. Chaos, Solitons & Fractals. 2020, 133 (4): 109638. Bibcode:2020CSF...13309638O. S2CID 118828500. arXiv:1901.09274 . doi:10.1016/j.chaos.2020.109638.
Gerig, A. Chaos in a one-dimensional compressible flow. Physical Review E. 2007, 75 (4): 045202. Bibcode:2007PhRvE..75d5202G. PMID 17500951. S2CID 45804559. arXiv:nlin/0701050 . doi:10.1103/PhysRevE.75.045202.
Liu, Yuansheng; Tang, Jie; Xie, Tao. Cryptanalyzing a RGB image encryption algorithm based on DNA encoding and chaos map. Optics & Laser Technology. 2014-08-01, 60: 111–115. Bibcode:2014OptLT..60..111L. S2CID 18740000. arXiv:1307.4279 . doi:10.1016/j.optlastec.2014.01.015.

books.google.com

Sprott 2003，第89頁
Weinberger, David. Everyday Chaos - Technology, Complexity, and How We're Thriving in a New World of Possibility. Harvard Business Review Press. 2019 [2023-11-15]. ISBN 9781633693968. （原始内容存档于2022-11-14）.

chaosbook.org

Feigenbaum, M. J. (1976) "Universality in complex discrete dynamics", Los Alamos Theoretical Division Annual Report 1975-1976 (PDF). [2023-11-14]. （原始内容存档 (PDF)于2010-12-14）.

cityu.edu.hk

ee.cityu.edu.hk

Chen, G.-R. Butterfly Effect and Chaos. (PDF). 2020-01-01 [2023-07-01]. （原始内容存档 (PDF)于2023-08-12）.

csessex.ac.uk

Nehmzow, Ulrich; Keith Walker. Quantitative description of robot–environment interaction using chaos theory (PDF). Robotics and Autonomous Systems. Dec 2005, 53 (3–4): 177–193 [2017-10-25]. CiteSeerX 10.1.1.105.9178 . doi:10.1016/j.robot.2005.09.009. （原始内容 (PDF)存档于2017-08-12）.

dictionary.com

Definition of chaos | Dictionary.com. www.dictionary.com. [2019-11-24]. （原始内容存档于2024-01-31）（英语）.

doi.org

Gardini, Laura; Grebogi, Celso; Lenci, Stefano. Chaos theory and applications: a retrospective on lessons learned and missed or new opportunities. Nonlinear Dynamics. 2020-10-01, 102 (2): 643–644. ISSN 1573-269X. doi:10.1007/s11071-020-05903-0 （英语）.
Poincaré, Jules Henri. Sur le problème des trois corps et les équations de la dynamique. Divergence des séries de M. Lindstedt. Acta Mathematica. 1890, 13 (1–2): 1–270. doi:10.1007/BF02392506 .
Kolmogorov, Andrey Nikolaevich. Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Doklady Akademii Nauk SSSR. 1941, 30 (4): 301–5. Bibcode:1941DoSSR..30..301K. Reprinted in: Kolmogorov, A. N. The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers. Proceedings of the Royal Society A. 1991, 434 (1890): 9–13. Bibcode:1991RSPSA.434....9K. S2CID 123612939. doi:10.1098/rspa.1991.0075.
Kolmogorov, A. N. On degeneration of isotropic turbulence in an incompressible viscous liquid. Doklady Akademii Nauk SSSR. 1941, 31 (6): 538–540. Reprinted in: Kolmogorov, A. N. Dissipation of Energy in the Locally Isotropic Turbulence. Proceedings of the Royal Society A. 1991, 434 (1890): 15–17. Bibcode:1991RSPSA.434...15K. S2CID 122060992. doi:10.1098/rspa.1991.0076.
Kolmogorov, A. N. Preservation of conditionally periodic movements with small change in the Hamilton function. Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics 98. 1979: 527–530. Bibcode:1979LNP....93...51K. ISBN 978-3-540-09120-2. doi:10.1007/BFb0021737. |journal=被忽略 (帮助) See also Kolmogorov–Arnold–Moser theorem
Cartwright, Mary L.; Littlewood, John E. On non-linear differential equations of the second order, I: The equation y" + k(1−y²)y' + y = bλkcos(λt + a), k large. Journal of the London Mathematical Society. 1945, 20 (3): 180–9. doi:10.1112/jlms/s1-20.3.180. See also: Van der Pol oscillator
Smale, Stephen. Morse inequalities for a dynamical system. Bulletin of the American Mathematical Society. January 1960, 66: 43–49. doi:10.1090/S0002-9904-1960-10386-2 .
Chirikov, B. V. Resonance processes in magnetic traps. The Soviet Journal of Atomic Energy. 1960-12-01, 6 (6): 464–470. ISSN 1573-8205. S2CID 59483478. doi:10.1007/BF01483352 （英语）.
Bellissard, J.; Bohigas, O.; Casati, G.; Shepelyansky, D.L. A pioneer of chaos. Physica D: Nonlinear Phenomena. 1 July 1999, 131 (1–4): viii–xv. Bibcode:1999PhyD..131D...8B. ISSN 0167-2789. S2CID 119107150. doi:10.1016/s0167-2789(99)90007-6.
Lorenz, Edward N. Deterministic non-periodic flow. Journal of the Atmospheric Sciences. 1963, 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 .
Berger J.M.; Mandelbrot B. A new model for error clustering in telephone circuits. IBM Journal of Research and Development. 1963, 7 (3): 224–236. doi:10.1147/rd.73.0224.
Mandelbrot, Benoît. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science. 5 May 1967, 156 (3775): 636–8 [2023-11-15]. Bibcode:1967Sci...156..636M. PMID 17837158. S2CID 15662830. doi:10.1126/science.156.3775.636. （原始内容存档于2021-10-19）.
Feigenbaum, Mitchell. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics. July 1978, 19 (1): 25–52. Bibcode:1978JSP....19...25F. CiteSeerX 10.1.1.418.9339 . S2CID 124498882. doi:10.1007/BF01020332.
Huberman, B.A. A Model for Dysfunctions in Smooth Pursuit Eye Movement. Annals of the New York Academy of Sciences. July 1987,. 504 Perspectives in Biological Dynamics and Theoretical Medicine (1): 260–273. Bibcode:1987NYASA.504..260H. PMID 3477120. S2CID 42733652. doi:10.1111/j.1749-6632.1987.tb48737.x.
Bak, Per; Tang, Chao; Wiesenfeld, Kurt. Self-organized criticality: An explanation of the 1/f noise. Physical Review Letters. 1987-07-27, 59 (4): 381–4. Bibcode:1987PhRvL..59..381B. PMID 10035754. S2CID 7674321. doi:10.1103/PhysRevLett.59.381. However, the conclusions of this article have been subject to dispute. ?. （原始内容存档于2007-12-14）. . See especially: Laurson, Lasse; Alava, Mikko J.; Zapperi, Stefano. Letter: Power spectra of self-organized critical sand piles. Journal of Statistical Mechanics: Theory and Experiment. 2005-09-15, 0511. L001.
Motter, A. E.; Campbell, D. K. Chaos at fifty. Phys. Today. 2013, 66 (5): 27–33. Bibcode:2013PhT....66e..27M. S2CID 54005470. arXiv:1306.5777 . doi:10.1063/pt.3.1977.
Hubler, A.; Foster, G.; Phelps, K. Managing chaos: Thinking out of the box. Complexity. 2007, 12 (3): 10. Bibcode:2007Cmplx..12c..10H. doi:10.1002/cplx.20159.
Kiel, L.; Elliott, Euel (编). Chaos Theory in the Social Sciences: Foundations and Applications. Ann Arbor, MI: University of Michigan Press. 1996. ISBN 9780472106387. doi:10.3998/mpub.14623. hdl:2027/fulcrum.d504rm03n （英语）.
Shen, Bo-Wen; Pielke, Sr., Roger; Zeng, Xubin. The 50th Anniversary of the Metaphorical Butterfly Effect since Lorenz (1972): Multistability, Multiscale Predictability, and Sensitivity in Numerical Models.. Atmosphere. 2023-08-12, 14 (8): 1279. Bibcode:2023Atmos..14.1279S. doi:10.3390/atmos14081279 .
Shen, Bo-Wen. A Review of Lorenz's Models from 1960 to 2008. International Journal of Bifurcation and Chaos. 2023-09-04, 33 (10): 2330024. doi:10.1142/S0218127423300240.
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Banks; Brooks; Cairns; Davis; Stacey. On Devaney's definition of chaos. The American Mathematical Monthly. 1992, 99 (4): 332–334. doi:10.1080/00029890.1992.11995856.
Vellekoop, Michel; Berglund, Raoul. On Intervals, Transitivity = Chaos. The American Mathematical Monthly. April 1994, 101 (4): 353–5. JSTOR 2975629. doi:10.2307/2975629.
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin. One Saddle Point and Two Types of Sensitivities within the Lorenz 1963 and 1969 Models. Atmosphere. 2022-05-07, 13 (5): 753. Bibcode:2022Atmos..13..753S. ISSN 2073-4433. doi:10.3390/atmos13050753  （英语）.
Werndl, Charlotte. What are the New Implications of Chaos for Unpredictability?. The British Journal for the Philosophy of Science. 2009, 60 (1): 195–220. S2CID 354849. arXiv:1310.1576 . doi:10.1093/bjps/axn053.
Li, T.Y.; Yorke, J.A. Period Three Implies Chaos (PDF). American Mathematical Monthly. 1975, 82 (10): 985–92. Bibcode:1975AmMM...82..985L. CiteSeerX 10.1.1.329.5038 . JSTOR 2318254. doi:10.2307/2318254. （原始内容 (PDF)存档于2009-12-29）.
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Shen, Bo-Wen. Aggregated Negative Feedback in a Generalized Lorenz Model. International Journal of Bifurcation and Chaos. 2019-03-01, 29 (3): 1950037–1950091. Bibcode:2019IJBC...2950037S. ISSN 0218-1274. S2CID 132494234. doi:10.1142/S0218127419500378 .
Shen, Bo-Wen; Pielke, Roger A.; Zeng, Xubin; Baik, Jong-Jin; Faghih-Naini, Sara; Cui, Jialin; Atlas, Robert. Is Weather Chaotic?: Coexistence of Chaos and Order within a Generalized Lorenz Model. Bulletin of the American Meteorological Society. 2021-01-01, 102 (1): E148–E158. Bibcode:2021BAMS..102E.148S. ISSN 0003-0007. S2CID 208369617. doi:10.1175/BAMS-D-19-0165.1  （英语）.
Shen, Bo-Wen; Pielke Sr., Roger Pielke; Zeng, Xubin; Cui, Jialin; Faghih-Naini, Sara; Paxson, Wei; Kesarkar, Amit; Zeng, Xiping; Atlas, Robert. The Dual Nature of Chaos and Order in the Atmosphere. Atmosphere. 2022-11-12, 13 (11): 1892. Bibcode:2022Atmos..13.1892S. ISSN 2073-4433. doi:10.3390/atmos13111892  （英语）.
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Shen, Bo-Wen; Pielke Sr., R. A.; Zeng, X.; Baik, J.-J.; Faghih-Naini, S.; Cui, J.; Atlas, R.; Reyes, T. A. L. Is Weather Chaotic? Coexisting Chaotic and Non-chaotic Attractors within Lorenz Models. Skiadas, Christos H.; Dimotikalis, Yiannis (编). 13th Chaotic Modeling and Simulation International Conference. Springer Proceedings in Complexity. Cham: Springer International Publishing. 2021: 805–825 [2023-11-14]. ISBN 978-3-030-70795-8. S2CID 245197840. doi:10.1007/978-3-030-70795-8_57. （原始内容存档于2023-05-28）（英语）.
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Shen, Bo-Wen. Nonlinear Feedback in a Five-Dimensional Lorenz Model. Journal of the Atmospheric Sciences. 2014-05-01, 71 (5): 1701–1723. Bibcode:2014JAtS...71.1701S. ISSN 0022-4928. S2CID 123683839. doi:10.1175/JAS-D-13-0223.1 （英语）.
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Okulov, A Yu. Structured light entities, chaos and nonlocal maps. Chaos, Solitons & Fractals. 2020, 133 (4): 109638. Bibcode:2020CSF...13309638O. S2CID 118828500. arXiv:1901.09274 . doi:10.1016/j.chaos.2020.109638.
Kyrtsou C.; Labys W. Evidence for chaotic dependence between US inflation and commodity prices. Journal of Macroeconomics. 2006, 28 (1): 256–266. doi:10.1016/j.jmacro.2005.10.019.
Kyrtsou C., Labys W.; Labys. Detecting positive feedback in multivariate time series: the case of metal prices and US inflation. Physica A. 2007, 377 (1): 227–229. Bibcode:2007PhyA..377..227K. doi:10.1016/j.physa.2006.11.002.
Hernández-Acosta, M. A.; Trejo-Valdez, M.; Castro-Chacón, J. H.; Miguel, C. R. Torres-San; Martínez-Gutiérrez, H. Chaotic signatures of photoconductive Cu 2 ZnSnS 4 nanostructures explored by Lorenz attractors. New Journal of Physics. 2018, 20 (2): 023048. Bibcode:2018NJPh...20b3048H. ISSN 1367-2630. doi:10.1088/1367-2630/aaad41  （英语）.
Hristu-Varsakelis, D.; Kyrtsou, C. Evidence for nonlinear asymmetric causality in US inflation, metal and stock returns. Discrete Dynamics in Nature and Society. 2008, 2008: 1–7. doi:10.1155/2008/138547 . 138547.
Kyrtsou, C.; M. Terraza. Is it possible to study chaotic and ARCH behaviour jointly? Application of a noisy Mackey-Glass equation with heteroskedastic errors to the Paris Stock Exchange returns series. Computational Economics. 2003, 21 (3): 257–276. S2CID 154202123. doi:10.1023/A:1023939610962.
Hubler, A.; Phelps, K. Guiding a self-adjusting system through chaos. Complexity. 2007, 13 (2): 62. Bibcode:2007Cmplx..13b..62W. doi:10.1002/cplx.20204.
Gerig, A. Chaos in a one-dimensional compressible flow. Physical Review E. 2007, 75 (4): 045202. Bibcode:2007PhRvE..75d5202G. PMID 17500951. S2CID 45804559. arXiv:nlin/0701050 . doi:10.1103/PhysRevE.75.045202.
Wotherspoon, T.; Hubler, A. Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map. The Journal of Physical Chemistry A. 2009, 113 (1): 19–22. Bibcode:2009JPCA..113...19W. PMID 19072712. doi:10.1021/jp804420g.
Borodkin, Leonid I. Challenges of Instability: The Concepts of Synergetics in Studying the Historical Development of Russia. Ural Historical Journal. 2019, 63 (2): 127–136. doi:10.30759/1728-9718-2019-2(63)-127-136 .
Dilão, R.; Domingos, T. Periodic and Quasi-Periodic Behavior in Resource Dependent Age Structured Population Models. Bulletin of Mathematical Biology. 2001, 63 (2): 207–230. PMID 11276524. S2CID 697164. doi:10.1006/bulm.2000.0213.
Akhavan, A.; Samsudin, A.; Akhshani, A. A symmetric image encryption scheme based on combination of nonlinear chaotic maps. Journal of the Franklin Institute. 2011-10-01, 348 (8): 1797–1813. doi:10.1016/j.jfranklin.2011.05.001.
Behnia, S.; Akhshani, A.; Mahmodi, H.; Akhavan, A. A novel algorithm for image encryption based on mixture of chaotic maps. Chaos, Solitons & Fractals. 2008-01-01, 35 (2): 408–419. Bibcode:2008CSF....35..408B. doi:10.1016/j.chaos.2006.05.011.
Wang, Xingyuan; Zhao, Jianfeng. An improved key agreement protocol based on chaos. Commun. Nonlinear Sci. Numer. Simul. 2012, 15 (12): 4052–4057. Bibcode:2010CNSNS..15.4052W. doi:10.1016/j.cnsns.2010.02.014.
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Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems, 2021, 5516703, https://www.hindawi.com/journals/mpe/2021/5516703/ （页面存档备份，存于互联网档案馆）
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jestr.org

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Edward Lorenz, father of chaos theory and butterfly effect, dies at 90. MIT News. 2008-04-16 [2019-11-24]. （原始内容存档于2024-01-18）.

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