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Diaz MMS, Trejo EJA, Martin DA, et al. Similar local neuronal dynamics may lead to different collective behavior. Phys Rev E. 2021;104(6):064309doi: 10.1103/PhysRevE.104.064309.
Diaz, M. M. S., Trejo, E. J. A., Martin, D. A., Cannas, S. A., Grigera, T. S., & Chialvo, D. R. (2021). Similar local neuronal dynamics may lead to different collective behavior. Physical review. E, 104(6), 064309. https://doi.org/10.1103/PhysRevE.104.064309
Diaz, Margarita M Sánchez, et al. "Similar local neuronal dynamics may lead to different collective behavior." Physical review. E vol. 104,6 (2021): 064309. doi: https://doi.org/10.1103/PhysRevE.104.064309
Diaz MMS, Trejo EJA, Martin DA, Cannas SA, Grigera TS, Chialvo DR. Similar local neuronal dynamics may lead to different collective behavior. Phys Rev E. 2021 Dec;104(6):064309. doi: 10.1103/PhysRevE.104.064309. PMID: 35030861.
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Phys Rev E. 2021 Dec;104(6):064309. doi: 10.1103/PhysRevE.104.064309.

Similar local neuronal dynamics may lead to different collective behavior.

Physical review. E

Margarita M Sánchez Diaz, Eyisto J Aguilar Trejo, Daniel A Martin, Sergio A Cannas, Tomás S Grigera, Dante R Chialvo

Affiliations

  1. Center for Complex Systems and Brain Sciences (CEMSC), Universidad Nacional de San Martín, Campus Miguelete, 25 de Mayo y Francia, 1650 San Martín, Buenos Aires, Argentina.
  2. Instituto de Ciencias Físicas (ICIFI), CONICET and Universidad Nacional de San Martín, 25 de Mayo y Francia, 1650 San Martín, Buenos Aires, Argentina.
  3. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Godoy Cruz 2290, 1425 Buenos Aires, Argentina.
  4. Instituto de Física Enrique Gaviola (IFEG-CONICET), Facultad de Matemática Astronomía Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina.
  5. Instituto de Física de Líquidos y Sistemas Biológicos (IFLySiB), CONICET and Universidad Nacional de La Plata, Calle 59 no. 789, B1900BTE La Plata, Buenos Aires, Argentina.
  6. Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Buenos Aires, Argentina.

PMID: 35030861 DOI: 10.1103/PhysRevE.104.064309

Abstract

This report is concerned with the relevance of the microscopic rules that implement individual neuronal activation, in determining the collective dynamics, under variations of the network topology. To fix ideas we study the dynamics of two cellular automaton models, commonly used, rather in-distinctively, as the building blocks of large-scale neuronal networks. One model, due to Greenberg and Hastings (GH), can be described by evolution equations mimicking an integrate-and-fire process, while the other model, due to Kinouchi and Copelli (KC), represents an abstract branching process, where a single active neuron activates a given number of postsynaptic neurons according to a prescribed "activity" branching ratio. Despite the apparent similarity between the local neuronal dynamics of the two models, it is shown that they exhibit very different collective dynamics as a function of the network topology. The GH model shows qualitatively different dynamical regimes as the network topology is varied, including transients to a ground (inactive) state, continuous and discontinuous dynamical phase transitions. In contrast, the KC model only exhibits a continuous phase transition, independently of the network topology. These results highlight the importance of paying attention to the microscopic rules chosen to model the interneuronal interactions in large-scale numerical simulations, in particular when the network topology is far from a mean-field description. One such case is the extensive work being done in the context of the Human Connectome, where a wide variety of types of models are being used to understand the brain collective dynamics.

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