IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v116y2018icp166-175.html
   My bibliography  Save this article

Complexity modeling and analysis of chaos and other fluctuating phenomena

Author

Listed:
  • Brechtl, Jamieson
  • Xie, Xie
  • Liaw, Peter K.
  • Zinkle, Steven J.

Abstract

The refined composite multiscale-entropy algorithm was applied to the time-dependent behavior of the Weierstrass functions, colored noise, and Logistic map to provide the fresh insight into the dynamics of these fluctuating phenomena. For the Weierstrass function, the complexity of fluctuations was found to increase with respect to the fractional dimension, D, of the graph. Additionally, the sample-entropy curves increased in an exponential fashion with increasing D. This increase in the complexity was found to correspond to a rising amount of irregularities in the oscillations. In terms of the colored noise, the complexity of the fluctuations was found to be the highest for the 1/f noise (f is the frequency of the generated noise), which is in agreement with findings in the literature. Moreover, the sample-entropy curves exhibited a decreasing trend for noise when the spectral exponent, β, was less than 1 and obeyed an increasing trend when β > 1. Importantly, a direct relationship was observed between the power-law exponents for the curves and the spectral exponents of the noise. For the logistic map, a correspondence was observed between the complexity maps and its bifurcation diagrams. Specifically, the map of the sample-entropy curves was negligible, when the bifurcation parameter, R, varied between 3 and 3.5. Beyond these values, the curves attained non-zero values that increased with increasing R, in general.

Suggested Citation

  • Brechtl, Jamieson & Xie, Xie & Liaw, Peter K. & Zinkle, Steven J., 2018. "Complexity modeling and analysis of chaos and other fluctuating phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 166-175.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:166-175
    DOI: 10.1016/j.chaos.2018.09.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918309329
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.09.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Grosjean, Nicolas & Huillet, Thierry, 2016. "Some combinatorial aspects of discrete non-linear population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 71-79.
    2. Rani, Mamta & Agarwal, Rashi, 2009. "A new experimental approach to study the stability of logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2062-2066.
    3. Liang, Y.S. & Su, W.Y., 2007. "The relationship between the fractal dimensions of a type of fractal functions and the order of their fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 682-692.
    4. Wang, Jing & Shang, Pengjian & Xia, Jianan & Shi, Wenbin, 2015. "EMD based refined composite multiscale entropy analysis of complex signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 583-593.
    5. Rocco, Andrea & West, Bruce J., 1999. "Fractional calculus and the evolution of fractal phenomena," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 535-546.
    6. Costa, M. & Peng, C.-K. & L. Goldberger, Ary & Hausdorff, Jeffrey M., 2003. "Multiscale entropy analysis of human gait dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 53-60.
    7. Poole, Marshall Scott & Van de Ven, Andrew H. & Dooley, Kevin & Holmes, Michael E., 2000. "Organizational Change and Innovation Processes: Theory and Methods for Research," OUP Catalogue, Oxford University Press, number 9780195131987.
    8. Zurek, Sebastian & Guzik, Przemyslaw & Pawlak, Sebastian & Kosmider, Marcin & Piskorski, Jaroslaw, 2012. "On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6601-6610.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yao, Wenpo & Yao, Wenli & Wang, Jun, 2021. "A novel parameter for nonequilibrium analysis in reconstructed state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Yu, Zihan & Deng, Yong, 2022. "Derive power law distribution with maximum Deng entropy," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Meng & Shang, Pengjian, 2018. "Analysis of financial time series using multiscale entropy based on skewness and kurtosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1543-1550.
    2. Yin, Yi & Shang, Pengjian & Feng, Guochen, 2016. "Modified multiscale cross-sample entropy for complex time series," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 98-110.
    3. Zhang, Ningning & Lin, Aijing & Ma, Hui & Shang, Pengjian & Yang, Pengbo, 2018. "Weighted multivariate composite multiscale sample entropy analysis for the complexity of nonlinear times series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 595-607.
    4. Liu, Yunxiao & Lin, Youfang & Wang, Jing & Shang, Pengjian, 2018. "Refined generalized multiscale entropy analysis for physiological signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 975-985.
    5. Tamer Khraisha & Keren Arthur, 2018. "Can we have a general theory of financial innovation processes? A conceptual review," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 4(1), pages 1-27, December.
    6. Jeffery S. McMullen & Dimo Dimov, 2013. "Time and the Entrepreneurial Journey: The Problems and Promise of Studying Entrepreneurship as a Process," Journal of Management Studies, Wiley Blackwell, vol. 50(8), pages 1481-1512, December.
    7. Gayoung Kim & Woo Jin Lee, 2021. "The Venture Firm’s Ambidexterity: Do Transformational Leaders Boost Organizational Learning for Venture Growth?," Sustainability, MDPI, vol. 13(15), pages 1-15, July.
    8. Restrepo, Juan F. & Schlotthauer, Gastón & Torres, María E., 2014. "Maximum approximate entropy and r threshold: A new approach for regularity changes detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 97-109.
    9. Geels, Frank W. & Ayoub, Martina, 2023. "A socio-technical transition perspective on positive tipping points in climate change mitigation: Analysing seven interacting feedback loops in offshore wind and electric vehicles acceleration," Technological Forecasting and Social Change, Elsevier, vol. 193(C).
    10. Jain, Sanjay, 2020. "Fumbling to the future? Socio-technical regime change in the recorded music industry," Technological Forecasting and Social Change, Elsevier, vol. 158(C).
    11. Fixson, Sebastian K. & Park, Jin-Kyu, 2008. "The power of integrality: Linkages between product architecture, innovation, and industry structure," Research Policy, Elsevier, vol. 37(8), pages 1296-1316, September.
    12. Kingshuk K. Sinha & Andrew H. Van de Ven, 2005. "Designing Work Within and Between Organizations," Organization Science, INFORMS, vol. 16(4), pages 389-408, August.
    13. Kriechbaum, Michael & Posch, Alfred & Hauswiesner, Angelika, 2021. "Hype cycles during socio-technical transitions: The dynamics of collective expectations about renewable energy in Germany," Research Policy, Elsevier, vol. 50(9).
    14. Kim, Yusoon & Choi, Thomas Y., 2021. "Supplier relationship strategies and outcome dualities: An empirical study of embeddedness perspective," International Journal of Production Economics, Elsevier, vol. 232(C).
    15. Yuanyuan Zhao, 2014. "Interpreting Innovation Dynamics with Complexity Theory," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 1-18.
    16. Rui Mu & Wouter Spekkink, 2018. "A Running Start or a Clean Slate? How a History of Cooperation Affects the Ability of Cities to Cooperate on Environmental Governance," Sustainability, MDPI, vol. 10(6), pages 1-22, June.
    17. Gjoko Stamenkov, 2023. "Recommendations for improving research quality: relationships among constructs, verbs in hypotheses, theoretical perspectives, and triangulation," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(3), pages 2923-2946, June.
    18. Natiq, Hayder & Banerjee, Santo & He, Shaobo & Said, M.R.M. & Kilicman, Adem, 2018. "Designing an M-dimensional nonlinear model for producing hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 506-515.
    19. Vaidheeswaran, Avinash & Rowan, Steven, 2021. "Chaos and recurrence analyses of pressure signals from bubbling fluidized beds," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Ram Kamath & Aitziber Elola & Frans Hermans, 2023. "The green-restructuring of clusters: investigating a biocluster's transition using a complex adaptive system model," European Planning Studies, Taylor & Francis Journals, vol. 31(9), pages 1842-1867, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:166-175. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.