Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units
Апстракт
We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the g...lobal variables of the exact system.
Извор:
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce, 2016, 1738Издавач:
- Amer Inst Physics, Melville
DOI: 10.1063/1.4951987
ISSN: 0094-243X
WoS: 000380803300224
Scopus: 2-s2.0-84984565458
Институција/група
PharmacyTY - CONF AU - Franović, Igor AU - Todorović, Kristina AU - Vasović, Nebojša AU - Burić, Nikola PY - 2016 UR - https://farfar.pharmacy.bg.ac.rs/handle/123456789/2665 AB - We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system. PB - Amer Inst Physics, Melville C3 - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce T1 - Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units VL - 1738 DO - 10.1063/1.4951987 ER -
@conference{ author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola", year = "2016", abstract = "We use the mean-field approach to analyze the collective dynamics in macroscopic networks of stochastic Fitzhugh-Nagumo units with delayed couplings. The conditions for validity of the two main approximations behind the model, called the Gaussian approximation and the Quasi-independence approximation, are examined. It is shown that the dynamics of the mean-field model may indicate in a self-consistent fashion the parameter domains where the Quasi-independence approximation fails. Apart from a network of globally coupled units, we also consider the paradigmatic setup of two interacting assemblies to demonstrate how our framework may be extended to hierarchical and modular networks. In both cases, the mean-field model can be used to qualitatively analyze the stability of the system, as well as the scenarios for the onset and the suppression of the collective mode. In quantitative terms, the mean-field model is capable of predicting the average oscillation frequency corresponding to the global variables of the exact system.", publisher = "Amer Inst Physics, Melville", journal = "Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce", title = "Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units", volume = "1738", doi = "10.1063/1.4951987" }
Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2016). Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units. in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce Amer Inst Physics, Melville., 1738. https://doi.org/10.1063/1.4951987
Franović I, Todorović K, Vasović N, Burić N. Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units. in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce. 2016;1738. doi:10.1063/1.4951987 .
Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Mean Field Dynamics of Networks of Delay-coupled Noisy Excitable Units" in Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2015 Proce, 1738 (2016), https://doi.org/10.1063/1.4951987 . .