### Abstract

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous 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 equations. 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 network and with the inclusion of the delay.

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

Article number | 58002 |

Number of pages | 9 |

Journal | Europhysics Letters |

Volume | 111 |

Issue number | 5 |

Publication status | Published - 18 Sep 2015 |

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### Keywords

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

### Cite this

*Europhysics Letters*,

*111*(5), [58002].

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*Europhysics Letters*, vol. 111, no. 5, 58002.

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

Research output: Contribution to journal › Article

TY - JOUR

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 - 2015/9/18

Y1 - 2015/9/18

N2 - A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous 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 equations. 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 network and with the inclusion of the delay.

AB - A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous 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 equations. 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 network and with the inclusion of the delay.

KW - nonlinear absorption

KW - spatio-temporal patterns

KW - Complex Networks

KW - delay differential equations

KW - Turing waves

UR - http://www.scopus.com/inward/record.url?scp=84944699057&partnerID=8YFLogxK

M3 - Article

VL - 111

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 5

M1 - 58002

ER -