### Abstract

We investigate the onset of collective oscillations in a excitatory pulse-coupled network of leaky integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O. V. Popovych , Phys. Rev. E 71 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N ->infinity, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogeneous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N-2, analogously to the scaling found for the "splay state.".

Original language | English |
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Article number | 046119 |

Number of pages | 7 |

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

Volume | 81 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2010 |

### Keywords

- pulse-coupled oscillators
- partial synchronization
- neurons

### Cite this

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

*81*(4), [046119]. https://doi.org/10.1103/PhysRevE.81.046119