Open AccessPattern selection of three components Gray-Scott model
Author(s) -
Huzaif Rahim,
Naveed Iqbal,
Cong Cong,
Zejun Ding
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1324/1/012012
Subject(s) - pattern formation , turing , reaction–diffusion system , gray (unit) , instability , homogeneous , nonlinear system , statistical physics , amplitude , computer science , mathematics , physics , mathematical analysis , mechanics , medicine , genetics , radiology , quantum mechanics , biology , programming language
The reaction-diffusion system demonstrates a variety of dynamical behaviours, and has become a standard model for explaining complex Turing patterns. In this work we have performed the analytical analysis of the three components Gray-Scott reaction-diffusion system. The analytical conditions for Turing instability about the homogeneous steady state has been derived. The linear stability is theoretically discussed. To determine the nature of pattern amplitude equation is derived by using weakly nonlinear analysis, which enumerates about the rich dynamical behaviour of this model, e.g. spot-, strip- and hexagon-patterns.