### 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 language | English |
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Article number | 036209 |

Number of pages | 9 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 80 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 2009 |

### Keywords

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

## Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*80*(3), [036209]. https://doi.org/10.1103/PhysRevE.80.036209