### Abstract

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

Publisher | Namur center for complex systems |

Number of pages | 9 |

Volume | 7 |

Edition | 15 |

Publication status | Published - 6 Jul 2015 |

### Publication series

Name | naXys Technical Report Series |
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Publisher | University of Namur |

No. | 15 |

Volume | 7 |

### Fingerprint

### Keywords

- nonlinear absorption
- spatio-temporal patterns
- Complex Networks
- delay differential equations
- Turing waves

### Cite this

*Delay induced Turing-like waves for one species reaction–diffusion model on a network*. (15 ed.) (naXys Technical Report Series; Vol. 7, No. 15). Namur center for complex systems.

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*Delay induced Turing-like waves for one species reaction–diffusion model on a network*. naXys Technical Report Series, no. 15, vol. 7, vol. 7, 15 edn, Namur center for complex systems.

**Delay induced Turing-like waves for one species reaction–diffusion model on a network.** / Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio.

Research output: Book/Report/Journal › Other report

TY - BOOK

T1 - Delay induced Turing-like waves for one species reaction–diffusion model on a network

AU - Petit, Julien

AU - Carletti, Timoteo

AU - Asllani, Malbor

AU - Fanelli, Duccio

PY - 2015/7/6

Y1 - 2015/7/6

N2 - A one species time–delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.

AB - A one species time–delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an external non homogenous perturbation. These are generalized Turing-like waves that materialize in a single species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time delayed differential equation. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz networks and with the inclusion of the delay.

KW - nonlinear absorption

KW - spatio-temporal patterns

KW - Complex Networks

KW - delay differential equations

KW - Turing waves

M3 - Other report

VL - 7

T3 - naXys Technical Report Series

BT - Delay induced Turing-like waves for one species reaction–diffusion model on a network

PB - Namur center for complex systems

ER -