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.
Pattern formation in a two-component reaction–diffusion system with delayed processes on a network / Petit, Julien; Asllani, Malbor; Fanelli, Duccio; Lauwens, Ben; Carletti, Timoteo. - In: PHYSICA. A. - ISSN 0378-4371. - STAMPA. - 462:(2016), pp. 230-249. [10.1016/j.physa.2016.06.003]
Pattern formation in a two-component reaction–diffusion system with delayed processes on a network
ASLLANI, MALBOR;FANELLI, DUCCIO;CARLETTI, TIMOTEO
2016
Abstract
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.File | Dimensione | Formato | |
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