### 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 |
---|---|

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

**Collective oscillations in disordered neural networks.** / Olmi, Simona; Livi, Roberto; Politi, Antonio; Torcini, Alessandro.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 81, no. 4, 046119. https://doi.org/10.1103/PhysRevE.81.046119

}

TY - JOUR

T1 - Collective oscillations in disordered neural networks

AU - Olmi, Simona

AU - Livi, Roberto

AU - Politi, Antonio

AU - Torcini, Alessandro

PY - 2010/4

Y1 - 2010/4

N2 - 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.".

AB - 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.".

KW - pulse-coupled oscillators

KW - partial synchronization

KW - neurons

U2 - 10.1103/PhysRevE.81.046119

DO - 10.1103/PhysRevE.81.046119

M3 - Article

VL - 81

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

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

SN - 1539-3755

IS - 4

M1 - 046119

ER -