### Abstract

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

Article number | 012303 |

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

Volume | 99 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2 Jan 2019 |

### Fingerprint

### Keywords

- chaos
- complex systems
- fluctuations and noise
- nonequilibrium statistical mechanics
- stochastic processes
- synchronization
- CHRONOTOPIC LYAPUNOV ANALYSIS
- STABILITY
- DYNAMICS

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

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

*99*(1), [012303]. https://doi.org/10.1103/PhysRevE.99.012303

**Desynchronization and pattern formation in a noisy feed-forward oscillator network.** / Zankoc, Clement (Corresponding Author); Fanelli, Duccio; Ginelli, Francesco; Livi, Roberto.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 99, no. 1, 012303. https://doi.org/10.1103/PhysRevE.99.012303

}

TY - JOUR

T1 - Desynchronization and pattern formation in a noisy feed-forward oscillator network

AU - Zankoc, Clement

AU - Fanelli, Duccio

AU - Ginelli, Francesco

AU - Livi, Roberto

N1 - The authors acknowledge financial support from H2020-MSCA-ITN-2015 project COSMOS 642563. We thank Arkady Pikovsky for useful comments.

PY - 2019/1/2

Y1 - 2019/1/2

N2 - We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non-normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node. If the lattice extends long enough, the initial synchrony gets eventually lost, and the system moves toward a non-trivial attractor, which can be analytically characterized as an asymptotic splay state. The noise assisted instability, ultimately vehiculated and amplified by the non-normal nature of the imposed couplings, eventually destabilizes also this second attractor. This phenomenon yields spatiotemporal patterns, which cannot be anticipated by a conventional linear stability analysis.

AB - We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non-normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node. If the lattice extends long enough, the initial synchrony gets eventually lost, and the system moves toward a non-trivial attractor, which can be analytically characterized as an asymptotic splay state. The noise assisted instability, ultimately vehiculated and amplified by the non-normal nature of the imposed couplings, eventually destabilizes also this second attractor. This phenomenon yields spatiotemporal patterns, which cannot be anticipated by a conventional linear stability analysis.

KW - chaos

KW - complex systems

KW - fluctuations and noise

KW - nonequilibrium statistical mechanics

KW - stochastic processes

KW - synchronization

KW - CHRONOTOPIC LYAPUNOV ANALYSIS

KW - STABILITY

KW - DYNAMICS

UR - http://www.scopus.com/inward/record.url?scp=85059804042&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/desynchronization-pattern-formation-noisy-feedforward-oscillator-network

U2 - 10.1103/PhysRevE.99.012303

DO - 10.1103/PhysRevE.99.012303

M3 - Article

VL - 99

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

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

SN - 1539-3755

IS - 1

M1 - 012303

ER -