Stability of splay states in globally coupled rotators

Massimo Calamai, Antonio Politi, Alessandro Torcini

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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

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