Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
arXiv:1603.07122 · doi:10.1016/j.physa.2016.06.003
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 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.
22 pages, 9 figures
References in corpus (6)
- Turing patterns in network-organized activator-inhibitor systems
- Pattern formation in multiplex networks
- Turing patterns in multiplex networks
- Some Special Cases in the Stability Analysis of Multi-Dimensional Time-Delay Systems Using The Matrix Lambert W function
- Delay induced Turing-like waves for one species reaction-diffusion model on a network
- Pattern formation for reactive species undergoing anisotropic diffusion