Application of Chaos Theory in Different Fields - A Literature Review

Authors

  • Adib Mashuri Department of General Studies, Batu Lanchang Vocational College, 11600 Jelutong, Pulau Pinang, Malaysia
  • Nur Hamiza Adenan Department of Mathematics, Faculty Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak, Malaysia
  • Nor Suriya Abd Karim Department of Mathematics, Faculty Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak, Malaysia
  • Siew Wei Tho Department of Physics, Faculty Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Tanjong Malim, Perak, Malaysia
  • Zhaofeng Zeng School of Physics and Electronic Engineering, Nanjiang Normal University, China

DOI:

https://doi.org/10.37134/jsml.vol12.1.11.2024

Keywords:

Chaos Theory, Dynamical System, Literature Review

Abstract

This comprehensive literature review delves into the multifaceted world of Chaos Theory and its pervasive applications across a wide spectrum of disciplines, including meteorology, economics, biology, engineering, medicine and social sciences. Chaos Theory's core principles, such as sensitivity to initial conditions and the discovery of hidden order within apparent chaos, are explored in-depth. This analysis delves into the intricate interconnections between Chaos Theory and dynamical systems, elucidating their shared objective of elucidating complex and dynamic phenomena. The research also investigates the application of the chaotic method as a problem-solving approach that acknowledges the inherent uncertainty and unpredictability of complex systems. The aforementioned approach is gaining traction in the realms of business, economics and the social sciences, despite facing criticism. The present study demonstrates the continued relevance of Chaos Theory in the contemporary era, as evidenced by its capacity to generate novel insights, provide comprehension of intricate scenarios and foster innovative advancements. The aforementioned aspect remains highly significant in addressing contemporary challenges and opportunities, as it profoundly influences our perception of the evolving global landscape in which we reside.

Downloads

Download data is not yet available.

References

Abarbanel HDI. (1996). Analysis of observed chaotic data. Springer New York.

Abel DL. (2009). The capabilities of chaos and complexity. International Journal of Molecular Sciences, 10(1), 247–291.

Adenan NH, Hamid NZA, Mohamed Z, Noorani MSM. (2017). A pilot study of river flow prediction in urban area based on phase space reconstruction. The 24th National Symposium on Mathematical Sciences (SKSM24), 1870, 040011.

Adenan NH, Karim NSA, Mashuri A, Hamid NZA, Adenan MS, Armansyah, Siregar I. (2021). Traffic flow prediction in urban area using inverse approach of chaos theory. Civil Engineering and Architecture, 9(4), 1277–1282.

Alexan W, Elbeltagy M, Aboshousha A. (2021). Image encryption through Lucas Sequence, S-Box and chaos theory. Proceedings - 2021 8th NAFOSTED Conference on Information and Computer Science, NICS 2021, 77–83.

Alligood KT, Sauer T, & Yorke JA. (1996). Chaos : an introduction to dynamical systems (1st ed.). Springer New York.

Biswas HR, Hasan MM, Bala SK. (2020). Chaos theory and its applications in our real life. Barishal University Journal Part 1, 5(1&2), 123–140.

Campbell DK. (2015). The pre-history of chaos-an interdisciplinary. Journal of Nonlinear Science Chaos, 25(9), 90401.

Debnath TK. (2022). The effect of chaos theory in the field of business: a review. International Journal Of Progressive Research In Science And Engineering, 3(5), 88–92.

Devaney RL, Keen L. (1989). Chaos and fractals: The mathematics behind the computer graphics. American Mathematical Society, Providence.

Gleick J. (2008). Chaos: making a new science. In Penguin Books.

Gupta V. (2022). Application of chaos theory for Arrhythmia detection in pathological databases. International Journal of Medical Engineering and Informatics, 15(2), 191–202.

Hadizadeh E, Taleghani M, Barari Nokashti S. (2022). Examining the forex market based on chaos theory. Journal of System Management, 8(3), 83–94.

Iirmdu TO. (2022). A chaos theory approach to understanding the impact of the COVID-19 Pandemic on tourism businesses in Plateau State, Nigeria. https://scholar.sun.ac.za

Iokibe T, Fujimoto Y, Kanke M, Suzuki S. (1997). Short-term prediction of chaotic time series by local fuzzy reconstruction method. Applications in Engineering and Technology, 5(1), 3–21.

Kantz H, Schreiber T. (2004). Nonlinear time series analysis. Cambridge University Press

Kaplan D, Glass L. (1995). Understanding nonlinear dynamics. Texts in Applied Mathematics, Springer New York.

Kiel LD, Elliott EW. (1996). Chaos theory in the social sciences: foundations and applications. In Chaos Theory in the Social Sciences. University of Michigan Press.

Klioutchnikov I, Sigova M, Beizerov N. (2017). Chaos theory in finance. Procedia Computer Science, 119, 368–375.

Kyriazis M. (2003). Practical applications of chaos theory to the modulation of human ageing: nature prefers chaos to regularity. Biogerontology, 4, 75–90.

Levy D. (1994). Chaos theory and strategy: theory, application, and managerial implications. Strategic Management Journal, 15(S2), 167–178.

Litimi H, Bensaïda A, Belkacem L, Abdallah O. (2019). Chaotic behavior in financial market volatility. Journal of Risk, 21(3), 27–54.

Lorenz EN. (1963). Deterministic nonperiodic flow. Journal Of The Atmospheric Sciences, 20, 12.

Mashuri A, Adenan NH, Karim SA, Shahriman A, Rani CNA. (2022). Performance of Water Level Forecasting Based on Chaos Approach Using Data Splitting. Environment and Ecology Research, 10(2), 218–224.

Mashuri A, Ali NM, Karim NSA, Ruslan AB, Adenan NH. (2023). The application of chaos theory on Covid-19 daily time series dataset in Malaysia. International Journal of Advanced Data Science and Intelligence Analytics, 3(1).

Mashuri A, Hamiza Adenan N, Suriya N, Karim A, Adenan S, Che N, Rani A. (2022). Performance of water level forecasting based on chaos approach using data splitting. Environment and Ecology Research, 10(2), 218–224.

Masnadi-Shirazi M, Subramaniam S. (2020). Attractor ranked radial basis function network: a nonparametric forecasting approach for chaotic dynamic systems. Scientific Reports, 10(1), 1–10.

Mesbahzadeh M. (2016). Applying the 0-1 test on the analysis of climate and weather data using chaos theory. Journal of Fundamental and Applied Sciences, 8(2), 1188.

Ott E. (2012). Chaos in dynamical systems. Cambridge University Press.

Owolabi KM. (2021). Numerical approach to chaotic Pattern Formation in Diffusive Predator–Prey System with Caputo Fractional Operator. Numerical Methods for Partial Differential Equations, 37(1), 131–151.

Pathak MD, Kar B, Panda MC. (2022). Chaos and Complexity: entrepreneurial Planning During Pandemic. Journal of Global Entrepreneurship Research, 12(1), 1–11.

Peckham M. (1980). Man’s Rage for Chaos: Biology, Behavior, and the Arts Paperback.

Peitgen HO, Jürgens H, Saupe D. (2004). Chaos and Fractals : New Frontiers of Science. Springer.

Popper K. (2002). The Logic of Scientific Discovery (2nd ed.).

Ruslan AB, Hamid NZA, Jusoh KC. (2020). Peramalan tak linear bagi siri masa karbon monoksida di kawasan dengan taburan penduduk tinggi di Sabah. Penerbit Universiti Kebangsaan Malaysia.

Sapini ML, Adam NS, Ibrahim N, Rosmen N, Yusof NM. (2017). The Presence of chaos in rainfall by using

-1 Test and Correlation Dimension. AIP Conference Proceedings, 1905(1), 050040.

Schemm S, Grund D, Knutti R, Wernli H, Ackermann M, Evensen, G. (2023). Learning from weather and climate science to prepare for a future pandemic. Proceedings of the National Academy of Sciences of the United States of America, 120(4), 1e2209091120.

Shen BW, Pielke RA, Zeng X, Baik JJ, Faghih NS, Cui J, Atlas R. (2021). Is weather chaotic?: coexistence of chaos and order within a Generalized Lorenz Model. Bulletin of the American Meteorological Society, 102(1), 148–158.

Soloviev V, Bielinskyi A, Serdyuk O, Solovieva V, Semerikov S. (2020). Lyapunov exponents as indicators of the stock market crashes.

Strogatz SH. (2018). Nonlinear dynamics and chaos. CRC press.

Sumiyana S, Sriwidharmanely S. (2020). Mitigating the harmful effects of technostress: inducing chaos theory in an experimental setting. Behaviour & Information Technology, 39(10), 1079–1093.

Tahir M, Tubaishat A, Al-Obeidat F, Shah B, Halim Z, Waqas M. (2022). A novel binary chaotic genetic algorithm for feature selection and its utility in affective computing and healthcare. Neural Computing and Applications, 34(14), 11453–11474.

Velickov S. (2004). Nonlinear dynamics and chaos. A.A.Balkema Publishers.

Wong MHY, Lee RST, Liu JNK. (2008). Wind shear forecasting by chaotic oscillatory-based neural networks (conn) with Lee Oscillator (retrograde signalling) model. Proceedings of the International Joint Conference on Neural Networks, 2040–2047.

Zakaria NH, Adenan NH, Karim NSA, Mashuri A. (2021). Prediction of water level time series data for dam at selangor using chaotic approach and local linear approximation method. Journal of Science and Mathematics Letters, 9, 10–17.

Zhang H, Dong JX. (2010). Chaos theory and its application in Modern Cryptography. ICCASM 2010 - 2010 International Conference on Computer Application and System Modeling, Proceedings.

Downloads

Published

2024-01-05

How to Cite

Mashuri, A., Adenan, N. H., Abd Karim, N. S., Tho, S. W., & Zeng, Z. (2024). Application of Chaos Theory in Different Fields - A Literature Review. Journal of Science and Mathematics Letters, 12(1), 92–101. https://doi.org/10.37134/jsml.vol12.1.11.2024

Issue

Section

Articles