Analysis of Principles and Applications of Chaos Theory
DOI:
https://doi.org/10.54097/kjjn4857Keywords:
Chaos; dynamics; complex systems; chaotic systems.Abstract
As early as Aristotle’s period, people were trying to find rules to define nature. Centuries later, there came Newton’s Laws of Motion, it was ‘omnipotent’ in explaining everything under gravitation, up to early twentieth century. Then, Einstein proposed theory of special relativity (responsible for everything else without gravitation), and general relativity (generalizing gravitation and special relativity). Nevertheless, along with order there is chaos. Chaos theory was not explicitly realized until late in the twentieth centuries, and that was when people realized that chaos is also capable of explaining the world. Computers are good with handling large data calculations, which the development of chaos theory benefits from. This study discusses some fundamental ideas of chaos theory, and focus on how they can be used to predict near futures in complex systems such as weather forecasting, stock markets, and transport systems. According to the analysis, there are also limitations, which again relates to computing technologies. However, the future is bright as advanced technologies await in the big data era.
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References
Thomas A. Utter Chaos. University of Cambridge, 2018.
Stewart I. Does God Play Dice. 2nd Edition. London: Penguin Books, 1997.
Chaotic Pendulum. Harvard University. Retrieved from: https://sciencedemonstrations.fas.harvard.edu/presentations/chaotic-pendulum#:~:text=A%20double%20pendulum%20executes%20simple,systems%20are%20not%20necessarily%20predictable.
Oestreicher C. A History of Chaos Theory. Dialogues Clin Neurosci, 2007-09, 9(3): 279-289.
Bishop R. Chaos. Stanford Encyclopedia of Philosophy. Retreved from: https://plato.stanford.edu/entries/chaos/#QuanDefCha
Aulbach B, Kieninger B. On Three Definitions of Chaos. Nonlinear Dynamics and Systems Theory, 2001, 1(1): 23-37.
Li T, Yorker J.A. Period Three Implies Chaos. The American Mathematical Monthly, 1975-12, 82(10): 985-992.
Blackmore D. The Mathematical Theory of Chaoas. Computers & Mathematics with Applications, 1986, 12(3-4): 1039-1045.
Hua Z, Zhou Y. One-Dimensional Nonlinear Model for Producing Chaos. Circuits and Systems I: Regular Paper, 2018-01, 65(1): 235-246.
Bhutta A A. Chaos, Fractlas & Their Real Life Applications. Applied Signal Processing, 1999-07-18.
Viswanath D. The Fractal Property of the Lonrenz Attractor. Physica D: Nonlinear Phenomena, 2004, 190(1-2): 115-128.
El-Basha O, El-Shahat A F, Fayed H. Chaos Theory and Lorenz Attractors. Sohag Journal of Sciences, 2016, 1: 1.
Department of physics, University of Oxford. Three Dimentional Systems Lecture 6: The Lorenz Equations. University of Oxford. Retrieved from: https://www2.physics.ox.ac.uk/sites/default/files/profiles/read/lect6-43147.pdf.
Lorenz Equations. MIT Retrieved from: https://dspace.mit.edu/bitstream/handle/1721.1/84612/12-006j-fall-2006/contents/lecture-notes/lecnotes11.pdf.
Ruelle D. Strange Attractors. Harvard University, Retrieved from: https://people.math.harvard.edu/~knill/teaching/mathe320_2014/blog/RuelleIntelligencer.pdf.
Sprott J C. Mandelbrot Set Chaos. Retrieved from: https://sprott.physics.wisc.edu/chaos/manchaos.htm.
Bauer P, Thorpe A, Brunet G. The Quiet Revolution of Numerical Weather Prediction. Nature, 2015, 525: 47-55.
Introduction to atomospheric dynamics. Atmospheric Dynamics Chapter 02 Part 01 Scale Analysis. Youtube, 2015-02-13. Retrieved from: https://www.youtube.com/watch?v=ROe7Wtn-l_M&t=182s.
Jaseena K U, Kovoor B C. Deterministic Weather Forecasting Models Based on Intelligent Predictors: A Survey. Journal of King Saud University – Computer and Information Sciences, 2022, 34(6-B): 3393-3412.
Miyoshi T, Sun Q. Control Simulation Experiment with Lorenz’s Butterfly Attractor. European Geosciences Union, 2022, 29(1): 133-139.
Klioutchnikov I, Sigova M, Beizerov N. Chaos Theory in Finance. Procedia Computer Science, 2017, 119: 368-375.
Łasak P, Wycislak S. Dynamics in Complex Systems Amidst Crists 2008+: Financial Regulatory and Supervisory Reflections. Risks, 2022, 10(2): 33.
Sumer K K. Do Financial Markets Exhibit Chaotic Behavior? Evidence from BIST, 2018: 93-101.
Wang S, He S, Yousefpour A, et al. Chaos and Complexity in a Fractional-Order Financial System with Time Delays. Chaos, Solitons & Fractals, 2020, 131.
Chen W. Nonlinear Dynamics and Chaos in a Fractional-Order Financial System. Chaos, Soitons & Fractals, 2008, 36(5): 1305-1314.
Abu-Shady M, Kaabar M K A. A Generalized Definition of the Fracitional Derivative with Appliactions. Advances in Mathematical Modeling of Flow Problems with Fractional Derivatives, 2021.
Blackledge J, Lamphiere M. A Review of the Fractal Market Hypothesis of Trading and Market Price Predictin. Mathematics, 2022, 10(1): 117.
Adewumi A, Kagamba J, Alochukwu A. Applications of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks. Safe, Resilient, and Substainable Transportation Systems, 2016.
Cheng A, Jiang X, Li Y, Zhang C, Zhu H. Multiple Sources and Multiple Measures Based Traffic Flow Prediction Using the Chaos Theory and Support Vector Regression Method. Physica A: Statistical Mechanics and Its Applications, 2017, 466: 422-434.
Liu H, Yang Y, Dai Z, Yu Z. The Largest Lyapunov Expnent of Chaotic Dynamical System in Scale Space and Its Application. Chaos, 2003-09, 13(3): 839-844.
Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 1993, 65(1-2): 117-134.
Parlitz U. Estimating Lyapunov Exponents from Time Series. Lecture Notes in Physics, 2016, 915.
Katambire V N, Musabe R, Uwitonze A, et al. Forecasting the Traffic Flow by Using ARIMA and LSTM Models: Case of Muhima Junction. Forecasting, 2023, 5(4): 616-618.
Kumar S V, Vanajakshi L. Short-term Traffic Flow Prediction Using Seasonal ARIMA Model with Limited Input Data. European Transport Research Review, 2015, 7.
Medina-Salgado B, Sánchez-DelaCruz E, Pozos-Parra P, et al. Urban Traffic Flow Prediction Techniques: A Review. Sustainable Computing: Informatics and Systems, 2022, 35.
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