### Abstract

We propose a dynamical gradient network approach to consider the synchronization in the Kuramoto model. Our scheme to adaptively adjust couplings is based on the dynamical gradient networks, where the number of links in each time interval is the same as the number of oscillators, but the links in different time intervals are also different. The gradient network in the (n+1)th time interval is decided by the oscillator dynamics in the nth time interval. According to the gradient network in the (n+1)th time interval, only one inlink's coupling for each oscillator is adjusted by a small incremental coupling. During the transition to synchronization, the intensities for all oscillators are identical. Direct numerical simulations fully verify that the synchronization in the Kuramoto model is realized effectively, even if there exist delayed couplings and external noise.

Original language | English |
---|---|

Article number | 027101 |

Number of pages | 4 |

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

Volume | 77 |

Issue number | 2 |

DOIs | |

Publication status | Published - 11 Feb 2008 |

### Cite this

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

*77*(2), [027101]. https://doi.org/10.1103/PhysRevE.77.027101

**Synchronization in the Kuramoto model : A dynamical gradient network approach.** / Chen, Maoyin; Shang, Yun; Zou, Yong; Kurths, Juergen.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 77, no. 2, 027101. https://doi.org/10.1103/PhysRevE.77.027101

}

TY - JOUR

T1 - Synchronization in the Kuramoto model

T2 - A dynamical gradient network approach

AU - Chen, Maoyin

AU - Shang, Yun

AU - Zou, Yong

AU - Kurths, Juergen

PY - 2008/2/11

Y1 - 2008/2/11

N2 - We propose a dynamical gradient network approach to consider the synchronization in the Kuramoto model. Our scheme to adaptively adjust couplings is based on the dynamical gradient networks, where the number of links in each time interval is the same as the number of oscillators, but the links in different time intervals are also different. The gradient network in the (n+1)th time interval is decided by the oscillator dynamics in the nth time interval. According to the gradient network in the (n+1)th time interval, only one inlink's coupling for each oscillator is adjusted by a small incremental coupling. During the transition to synchronization, the intensities for all oscillators are identical. Direct numerical simulations fully verify that the synchronization in the Kuramoto model is realized effectively, even if there exist delayed couplings and external noise.

AB - We propose a dynamical gradient network approach to consider the synchronization in the Kuramoto model. Our scheme to adaptively adjust couplings is based on the dynamical gradient networks, where the number of links in each time interval is the same as the number of oscillators, but the links in different time intervals are also different. The gradient network in the (n+1)th time interval is decided by the oscillator dynamics in the nth time interval. According to the gradient network in the (n+1)th time interval, only one inlink's coupling for each oscillator is adjusted by a small incremental coupling. During the transition to synchronization, the intensities for all oscillators are identical. Direct numerical simulations fully verify that the synchronization in the Kuramoto model is realized effectively, even if there exist delayed couplings and external noise.

U2 - 10.1103/PhysRevE.77.027101

DO - 10.1103/PhysRevE.77.027101

M3 - Article

VL - 77

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

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

SN - 1539-3755

IS - 2

M1 - 027101

ER -