Projects per year

### 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 |

### 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

## Activities

## Control of self-organized patterns in complex networks

Timoteo Carletti (Speaker)

Activity: Participating in or organising an event types › Participation in workshop, seminar, course

## Control of self-organized patterns in complex networks

Timoteo Carletti (Organiser)

Activity: Participating in or organising an event types › Participation in workshop, seminar, course

## IAP VIII / 19 DYSCO - Dynamical SYStems Control and Optimization DYSCO Study day

Timoteo Carletti (Speaker)

Activity: Participating in or organising an event types › Participation to a Symposium, a study Day

## Cite this

*Europhysics Letters*,

*111*(5), [58002].