Projects per year

### Abstract

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.

Original language | English |
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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 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Delay induced Turing-like waves for one species reaction–diffusion model on a network'. Together they form a unique fingerprint.

## Projects

## PAI n°P7/19 - DYSCO: Dynamical systems, control and optimization (DYSCO)

WINKIN, J., Blondel, V., Vandewalle, J., Pintelon, R., Sepulchre, R., Vande Wouwer, A. & SARTENAER, A.

1/04/12 → 30/09/17

Project: Research

## Equipment

## High Performance Computing Technology Platform

Benoît Champagne (Manager)

Technological Platform High Performance ComputingFacility/equipment: Technological Platform

## Cite this

Petit, J., Carletti, T., Asllani, M., & Fanelli, D. (2015).

*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.