IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v487y2017icp111-124.html
   My bibliography  Save this article

Collective dynamics in heterogeneous networks of neuronal cellular automata

Author

Listed:
  • Manchanda, Kaustubh
  • Bose, Amitabha
  • Ramaswamy, Ramakrishna

Abstract

We examine the collective dynamics of heterogeneous random networks of model neuronal cellular automata. Each automaton has b active states, a single silent state and r−b−1 refractory states, and can show ‘spiking’ or ‘bursting’ behavior, depending on the values of b. We show that phase transitions that occur in the dynamical activity can be related to phase transitions in the structure of Erdõs–Rényi graphs as a function of edge probability. Different forms of heterogeneity allow distinct structural phase transitions to become relevant. We also show that the dynamics on the network can be described by a semi-annealed process and, as a result, can be related to the Boolean Lyapunov exponent.

Suggested Citation

  • Manchanda, Kaustubh & Bose, Amitabha & Ramaswamy, Ramakrishna, 2017. "Collective dynamics in heterogeneous networks of neuronal cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 111-124.
    • Handle: RePEc:eee:phsmap:v:487:y:2017:i:c:p:111-124
    DOI: 10.1016/j.physa.2017.06.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117306623
    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.2017.06.021?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. Burstedde, C & Klauck, K & Schadschneider, A & Zittartz, J, 2001. "Simulation of pedestrian dynamics using a two-dimensional cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 507-525.
    2. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    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. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
    2. Chen, Changkun & Sun, Huakai & Lei, Peng & Zhao, Dongyue & Shi, Congling, 2021. "An extended model for crowd evacuation considering pedestrian panic in artificial attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    3. Jorge Peña & Yannick Rochat, 2012. "Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    4. Yue, Hao & Zhang, Junyao & Chen, Wenxin & Wu, Xinsen & Zhang, Xu & Shao, Chunfu, 2021. "Simulation of the influence of spatial obstacles on evacuation pedestrian flow in walking facilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    5. Tamás Nepusz & Tamás Vicsek, 2013. "Hierarchical Self-Organization of Non-Cooperating Individuals," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-9, December.
    6. Aslam, Faheem & Aziz, Saqib & Nguyen, Duc Khuong & Mughal, Khurrum S. & Khan, Maaz, 2020. "On the efficiency of foreign exchange markets in times of the COVID-19 pandemic," Technological Forecasting and Social Change, Elsevier, vol. 161(C).
    7. Tanimoto, Jun & Hagishima, Aya & Tanaka, Yasukaka, 2010. "Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5611-5618.
    8. Jiang, Jingchi & Zheng, Jichuan & Zhao, Chao & Su, Jia & Guan, Yi & Yu, Qiubin, 2016. "Clinical-decision support based on medical literature: A complex network approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 42-54.
    9. Liu, Zhichen & Li, Ying & Zhang, Zhaoyi & Yu, Wenbo, 2022. "A new evacuation accessibility analysis approach based on spatial information," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    10. Liu, Qian, 2018. "A social force model for the crowd evacuation in a terrorist attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 315-330.
    11. Liu, Jing & Jia, Yang & Mao, Tianlu & Wang, Zhaoqi, 2022. "Modeling and simulation analysis of crowd evacuation behavior under terrorist attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. Zheng, Xiaoping & Cheng, Yuan, 2011. "Conflict game in evacuation process: A study combining Cellular Automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1042-1050.
    13. Gerhardt, Günther J.L. & Lemke, Ney & Corso, Gilberto, 2006. "Network clustering coefficient approach to DNA sequence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1037-1045.
    14. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    15. Korbmacher, Raphael & Dang, Huu-Tu & Tordeux, Antoine, 2024. "Predicting pedestrian trajectories at different densities: A multi-criteria empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    16. Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    17. Liu, X. & Murata, T., 2010. "Advanced modularity-specialized label propagation algorithm for detecting communities in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1493-1500.
    18. Xie, Chuan-Zhi & Tang, Tie-Qiao & Hu, Peng-Cheng & Chen, Liang, 2022. "Observation and cellular-automaton based modeling of pedestrian behavior on an escalator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    19. Wen, Xiangxi & Tu, Congliang & Wu, Minggong, 2018. "Node importance evaluation in aviation network based on “No Return” node deletion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 546-559.
    20. Huang, Qi & Qin, Tianyu & Luo, Lin & Yang, Gaobo & Fu, Zhijian & Liu, Xiaobo, 2024. "Modeling heterogenous crowd evacuation on stairs in high-rise buildings using a fine discrete floor field cellular automaton model: Accounting for speed and boundary layer variations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).

    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:487:y:2017:i:c:p:111-124. 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.