Pattern formation in a two-component reaction–diffusion system with delayed processes on a network

Julien Petit, Malbor Asllani, Duccio Fanelli, Ben Lauwens, Timoteo Carletti

Research output: Contribution to journalArticlepeer-review


Reaction–diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts

whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overcome the respective limitations of the single-species case with delay, and that of the classical activator–inhibitor variant without delay. Numerical results gained from the Mimura–Murray model support the theoretical approach.

Original languageEnglish
Pages (from-to)230-249
Number of pages20
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 17 Jun 2016


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

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