WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 12, 2013
Turing Instability for a Two Dimensional Semi-Discrete Gray-Scott System
Authors: , , ,
Abstract: This paper is concerned with the spatial patterns of the Gray-Scott system which describes a general two- variable kinetic model that represents an activator-substrate scheme, where the space is discrete in two dimensions with the periodic boundary conditions and the time is continuous. Furthermore conditions for producing Turing instability of a general semi-discrete system are obtained through linear stability analysis and this conclusion is applied to the semi-discrete G-S model. Then in the Turing instability region of semi-discrete G-S model, we perform a series of numerical simulations which shown that this system can produce some new Turing patterns such as striped, spotted and lace-liked patterns in the Turing instability region. In particular, the observation of Turing patterns are reported, as a control parameter is varied, from a spatially uniform state to a patterned state. It suggests that the values of parameters make a great impact on Turing patterns.
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Keywords: Semi-discrete, Gray-Scott model, Turing instability, Turing pattern, Diffusion, Pattern formation