Issue |
EPL
Volume 111, Number 5, September 2015
|
|
---|---|---|
Article Number | 58002 | |
Number of page(s) | 6 | |
Section | Interdisciplinary Physics and Related Areas of Science and Technology | |
DOI | https://doi.org/10.1209/0295-5075/111/58002 | |
Published online | 21 September 2015 |
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
1 naXys, Namur Center for Complex Systems, University of Namur - rempart de la Vierge 8, B 5000 Namur, Belgium
2 Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC - Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy
Received: 8 July 2015
Accepted: 31 August 2015
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.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.Kd – Patterns / 89.75.Fb – Structures and organization in complex systems
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.