IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v77y2015icp215-224.html
   My bibliography  Save this article

A gradient flow approach to the model of positive feedback in decision-making

Author

Listed:
  • Zabzina, Natalia

Abstract

Recent studies on social dynamics have been done by using tools and methods of physics and economics. The main idea is that the regularity observed on a global scale arises out of local interactions between the group members. We consider the model describing one of the major interaction mechanism, the model of positive feedback. We propose a geometrical reformulation of this model in terms of gradient flow equations on a Riemannian manifold. The benefit of this reformulation is that we introduce an alternative method to study phenomena of the well known model. We suggest the analogy with a particle moving on curved manifold. We believe that this analogy will allow us to extend powerful mathematical tools from analytical mechanics to the biological systems.

Suggested Citation

  • Zabzina, Natalia, 2015. "A gradient flow approach to the model of positive feedback in decision-making," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 215-224.
    • Handle: RePEc:eee:chsofr:v:77:y:2015:i:c:p:215-224
    DOI: 10.1016/j.chaos.2015.05.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915001630
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.05.027?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. Stamatios C Nicolis & Natalia Zabzina & Tanya Latty & David J T Sumpter, 2011. "Collective Irrationality and Positive Feedback," PLOS ONE, Public Library of Science, vol. 6(4), pages 1-6, April.
    2. Teppo Felin & David J.T. Sumpter & Natalia Zabzina & Stamatios C. Nicolis, 2012. "Six Predictions about the Decision Making of Animal and Human Groups," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 33(5-6), pages 295-309, July.
    3. Czirók, András & Vicsek, Tamás, 2000. "Collective behavior of interacting self-propelled particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 17-29.
    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. Dussutour, Audrey & Nicolis, Stamatios C., 2013. "Flexibility in collective decision-making by ant colonies: Tracking food across space and time," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 32-38.
    2. Natalia Zabzina & Audrey Dussutour & Richard P Mann & David J T Sumpter & Stamatios C Nicolis, 2014. "Symmetry Restoring Bifurcation in Collective Decision-Making," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-11, December.
    3. Becco, Ch. & Vandewalle, N. & Delcourt, J. & Poncin, P., 2006. "Experimental evidences of a structural and dynamical transition in fish school," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 487-493.
    4. Huepe, Cristián & Aldana, Maximino, 2008. "New tools for characterizing swarming systems: A comparison of minimal models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2809-2822.
    5. Minsung Kim & Minki Kim, 2014. "Group-Wise Herding Behavior in Financial Markets: An Agent-Based Modeling Approach," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-7, April.
    6. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2012. "Admissible consensus and consensualization of high-order linear time-invariant singular swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5839-5849.
    7. Xi, Jianxiang & Yao, Zhicheng & Wang, Zhong & Liu, Guangbin & Zhong, Yisheng, 2014. "Admissible L2 consensus for singular time-delayed swarm systems with external disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 165-176.
    8. Liu, Bo & Chu, Tianguang & Wang, Long & Wang, Zhanfeng, 2008. "Collective motion of a class of social foraging swarms," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 277-292.
    9. Ibrahim Filiz & Thomas Nahmer & Markus Spiwoks & Kilian Bizer, 2018. "Portfolio diversification: the influence of herding, status-quo bias, and the gambler’s fallacy," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 32(2), pages 167-205, May.
    10. Barbaro, Alethea B.T. & Taylor, Kirk & Trethewey, Peterson F. & Youseff, Lamia & Birnir, Björn, 2009. "Discrete and continuous models of the dynamics of pelagic fish: Application to the capelin," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(12), pages 3397-3414.
    11. Xi, Jianxiang & Cai, Ning & Zhong, Yisheng, 2010. "Consensus problems for high-order linear time-invariant swarm systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5619-5627.
    12. Filiz, Ibrahim & Nahmer, Thomas & Spiwoks, Markus, 2019. "Herd behavior and mood: An experimental study on the forecasting of share prices," Journal of Behavioral and Experimental Finance, Elsevier, vol. 24(C).
    13. Mirabet, Vincent & Auger, Pierre & Lett, Christophe, 2007. "Spatial structures in simulations of animal grouping," Ecological Modelling, Elsevier, vol. 201(3), pages 468-476.
    14. Teppo Felin & Teppo Felin, 2012. "Cosmologies of Capability, Markets and Wisdom of Crowds: Introduction and Comparative Agenda," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 33(5-6), pages 283-294, July.
    15. Ye Yuan & Xuebo Chen & Qiubai Sun & Tianyun Huang, 2017. "Analysis of topological relationships and network properties in the interactions of human beings," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-22, August.
    16. Mu, Shumei & Chu, Tianguang & Wang, Long, 2005. "Coordinated collective motion in a motile particle group with a leader," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 211-226.
    17. Collet, Jacques Henri, 2007. "Order–disorder alternations in the populations of faulty repulsive agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 345-364.
    18. Xi, Jianxiang & Shi, Zongying & Zhong, Yisheng, 2011. "Consensus analysis and design for high-order linear swarm systems with time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4114-4123.

    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:77:y:2015:i:c:p:215-224. 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.