Stability of splay states in globally coupled rotators

Massimo Calamai, Antonio Politi, Alessandro Torcini

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet exponent scale as 1/N-2. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than 1/N-2 (namely, as 1/N-4) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].

Original languageEnglish
Article number036209
Number of pages9
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume80
Issue number3
DOIs
Publication statusPublished - Sep 2009

Keywords

  • neurophysiology
  • nonlinear dynamical systems
  • physiological models
  • stability
  • Josephson arrays
  • oscillators
  • synchronization
  • networks
  • laser

Cite this

Stability of splay states in globally coupled rotators. / Calamai, Massimo; Politi, Antonio; Torcini, Alessandro.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 80, No. 3, 036209, 09.2009.

Research output: Contribution to journalArticle

@article{6890c9286d084dc289e7b495e322ed49,
title = "Stability of splay states in globally coupled rotators",
abstract = "The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet exponent scale as 1/N-2. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than 1/N-2 (namely, as 1/N-4) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].",
keywords = "neurophysiology, nonlinear dynamical systems, physiological models, stability, Josephson arrays, oscillators, synchronization, networks, laser",
author = "Massimo Calamai and Antonio Politi and Alessandro Torcini",
year = "2009",
month = "9",
doi = "10.1103/PhysRevE.80.036209",
language = "English",
volume = "80",
journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",
issn = "1539-3755",
publisher = "AMER PHYSICAL SOC",
number = "3",

}

TY - JOUR

T1 - Stability of splay states in globally coupled rotators

AU - Calamai, Massimo

AU - Politi, Antonio

AU - Torcini, Alessandro

PY - 2009/9

Y1 - 2009/9

N2 - The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet exponent scale as 1/N-2. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than 1/N-2 (namely, as 1/N-4) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].

AB - The stability of dynamical states characterized by a uniform firing rate (splay states) is analyzed in a network of N globally pulse-coupled rotators (neurons) subject to a generic velocity field. In particular, we analyze short-wavelength modes that were known to be marginally stable in the infinite N limit and show that the corresponding Floquet exponent scale as 1/N-2. Moreover, we find that the sign, and thereby the stability, of this spectral component is determined by the sign of the average derivative of the velocity field. For leaky-integrate-and-fire neurons, an analytic expression for the whole spectrum is obtained. In the intermediate case of continuous velocity fields, the Floquet exponents scale faster than 1/N-2 (namely, as 1/N-4) and we even find strictly neutral directions in a wider class than the sinusoidal velocity fields considered by Watanabe and Strogatz [Physica D 74, 197 (1994)].

KW - neurophysiology

KW - nonlinear dynamical systems

KW - physiological models

KW - stability

KW - Josephson arrays

KW - oscillators

KW - synchronization

KW - networks

KW - laser

U2 - 10.1103/PhysRevE.80.036209

DO - 10.1103/PhysRevE.80.036209

M3 - Article

VL - 80

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 3

M1 - 036209

ER -