期刊
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
卷 462, 期 -, 页码 230-249出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2016.06.003
关键词
Turing patterns; Nonlinear dynamics; Spatio-temporal patterns; Complex networks; Delay differential equations
资金
- Interuniversity Attraction Poles Programme
- Belgian State, Science Policy Office
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. (C) 2016 Elsevier B.V. All rights reserved.
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