IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v382y2007i1p302-310.html
   My bibliography  Save this article

Periodic attractors of random truncator maps

Author

Listed:
  • Theodosopoulos, Ted
  • Boyer, Robert

Abstract

This paper introduces the truncator map as a dynamical system on the space of configurations of an interacting particle system. We represent the symbolic dynamics generated by this system as a non-commutative algebra and classify its periodic orbits using properties of endomorphisms of the resulting algebraic structure. A stochastic model is constructed on these endomorphisms, which leads to the classification of the distribution of periodic orbits for random truncator maps. This framework is applied to investigate the periodic transitions of Bornholdt's spin market model.

Suggested Citation

  • Theodosopoulos, Ted & Boyer, Robert, 2007. "Periodic attractors of random truncator maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 302-310.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:302-310
    DOI: 10.1016/j.physa.2007.02.090
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107002312
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.02.090?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. Theodosopoulos, Ted & Yuen, Ming, 2007. "Properties of the wealth process in a market microstructure model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 443-452.
    2. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    3. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
    4. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.
    Full references (including those not matched with items on IDEAS)

    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. Jørgen Vitting Andersen & Ioannis Vrontos & Petros Dellaportas & Serge Galam, 2014. "Communication impacting financial markets," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00982959, HAL.
    2. Yue Chen & Xiaojian Niu & Yan Zhang, 2019. "Exploring Contrarian Degree in the Trading Behavior of China's Stock Market," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    3. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    4. Torsten Trimborn & Philipp Otte & Simon Cramer & Maximilian Beikirch & Emma Pabich & Martin Frank, 2020. "SABCEMM: A Simulator for Agent-Based Computational Economic Market Models," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 707-744, February.
    5. Tetsuya Takaishi, 2016. "Dynamical cross-correlation of multiple time series Ising model," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 455-468, December.
    6. Ted Theodosopoulos, 2004. "Uncertainty relations in models of market microstructure," Papers math/0409076, arXiv.org, revised Feb 2005.
    7. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    8. Kei Katahira & Yu Chen, 2019. "Heterogeneous wealth distribution, round-trip trading and the emergence of volatility clustering in Speculation Game," Papers 1909.03185, arXiv.org.
    9. Kristoufek, Ladislav & Vošvrda, Miloslav S., 2016. "Herding, minority game, market clearing and efficient markets in a simple spin model framework," FinMaP-Working Papers 68, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    10. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    11. Simon Cramer & Torsten Trimborn, 2019. "Stylized Facts and Agent-Based Modeling," Papers 1912.02684, arXiv.org.
    12. Cross, Rod & Grinfeld, Michael & Lamba, Harbir & Seaman, Tim, 2005. "A threshold model of investor psychology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 463-478.
    13. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    14. Kukacka, Jiri & Barunik, Jozef, 2013. "Behavioural breaks in the heterogeneous agent model: The impact of herding, overconfidence, and market sentiment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5920-5938.
    15. Kei Katahira & Yu Chen & Gaku Hashimoto & Hiroshi Okuda, 2019. "Development of an agent-based speculation game for higher reproducibility of financial stylized facts," Papers 1902.02040, arXiv.org.
    16. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2020. "Robust Mathematical Formulation And Probabilistic Description Of Agent-Based Computational Economic Market Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-41, September.
    17. Tetsuya Takaishi, 2008. "Financial Time Series Analysis of SV Model by Hybrid Monte Carlo," Papers 0807.4394, arXiv.org.
    18. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    19. Theodosopoulos, Ted, 2005. "Uncertainty relations in models of market microstructure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 209-216.
    20. Meudt, Frederik & Schmitt, Thilo A. & Schäfer, Rudi & Guhr, Thomas, 2016. "Equilibrium pricing in an order book environment: Case study for a spin model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 228-235.

    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:phsmap:v:382:y:2007:i:1:p:302-310. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.