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Mean-field approximation of two coupled populations of excitable units

Authorized Users Only
2013
Authors
Franović, Igor
Todorović, Kristina
Vasović, Nebojša
Burić, Nikola
Article (Published version)
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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 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

Source:
Physical Review E, 2013, 87, 1
Publisher:
  • Amer Physical Soc, College Pk
Projects:
  • Modeling and Numerical Simulations of Complex Many-Body Systems (RS-171017)

DOI: 10.1103/PhysRevE.87.012922

ISSN: 2470-0045

PubMed: 23410419

WoS: 000314342700011

Scopus: 2-s2.0-84873602674
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URI
http://farfar.pharmacy.bg.ac.rs/handle/123456789/1948
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