Mean-field approximation of two coupled populations of excitable units
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2013
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The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains whe...re the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings. DOI: 10.1103/PhysRevE.87.012922
Izvor:
Physical Review E, 2013, 87, 1Izdavač:
- Amer Physical Soc, College Pk
Finansiranje / projekti:
- Modeliranje i numeričke simulacije složenih višečestičnih sistema (RS-MESTD-Basic Research (BR or ON)-171017)
DOI: 10.1103/PhysRevE.87.012922
ISSN: 2470-0045
PubMed: 23410419
WoS: 000314342700011
Scopus: 2-s2.0-84873602674
Institucija/grupa
PharmacyTY - JOUR AU - Franović, Igor AU - Todorović, Kristina AU - Vasović, Nebojša AU - Burić, Nikola PY - 2013 UR - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1948 AB - The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings. DOI: 10.1103/PhysRevE.87.012922 PB - Amer Physical Soc, College Pk T2 - Physical Review E T1 - Mean-field approximation of two coupled populations of excitable units VL - 87 IS - 1 DO - 10.1103/PhysRevE.87.012922 ER -
@article{ author = "Franović, Igor and Todorović, Kristina and Vasović, Nebojša and Burić, Nikola", year = "2013", abstract = "The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations composed of N stochastic excitable units each is performed by studying an approximate system, obtained by replacing each population with the corresponding mean-field model. In the exact system, one has the units within an ensemble communicating via the time-delayed linear couplings, whereas the interensemble terms involve the nonlinear time-delayed interaction mediated by the appropriate global variables. The aim is to demonstrate that the bifurcations affecting the stability of the stationary state of the original system, governed by a set of 4N stochastic delay-differential equations for the microscopic dynamics, can accurately be reproduced by a flow containing just four deterministic delay-differential equations which describe the evolution of the mean-field based variables. In particular, the considered issues include determining the parameter domains where the stationary state is stable, the scenarios for the onset, and the time-delay induced suppression of the collective mode, as well as the parameter domains admitting bistability between the equilibrium and the oscillatory state. We show how analytically tractable bifurcations occurring in the approximate model can be used to identify the characteristic mechanisms by which the stationary state is destabilized under different system configurations, like those with symmetrical or asymmetrical interpopulation couplings. DOI: 10.1103/PhysRevE.87.012922", publisher = "Amer Physical Soc, College Pk", journal = "Physical Review E", title = "Mean-field approximation of two coupled populations of excitable units", volume = "87", number = "1", doi = "10.1103/PhysRevE.87.012922" }
Franović, I., Todorović, K., Vasović, N.,& Burić, N.. (2013). Mean-field approximation of two coupled populations of excitable units. in Physical Review E Amer Physical Soc, College Pk., 87(1). https://doi.org/10.1103/PhysRevE.87.012922
Franović I, Todorović K, Vasović N, Burić N. Mean-field approximation of two coupled populations of excitable units. in Physical Review E. 2013;87(1). doi:10.1103/PhysRevE.87.012922 .
Franović, Igor, Todorović, Kristina, Vasović, Nebojša, Burić, Nikola, "Mean-field approximation of two coupled populations of excitable units" in Physical Review E, 87, no. 1 (2013), https://doi.org/10.1103/PhysRevE.87.012922 . .