期刊
APPLIED MATHEMATICAL MODELLING
卷 46, 期 -, 页码 476-491出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2017.01.081
关键词
Gierer-Meinhardt model; Turing bifurcation; Pattern formation; Fourier transform; Amplitude equations; Saturating term
资金
- National Natural Science Foundation of China [11571257, 11101076]
- Scientific Research Start-up Foundation of Hangzhou Normal University [201603]
Gierer-Meinhardt system is a typical mathematical model to describe chemical and biological phenomena. In this paper, the Gierer-Meinhardt model with a saturating term is considered. By the linear stability analysis, we find the parameter area where possible Turing instability can occur. Then the multiple scales method is applied to obtain the amplitude equations at the critical value of Turing bifurcation, which help us to derive parameter space more specific where certain patterns such as spot-like pattern, stripe-like pattern and the coexistence pattern will emerge. Furthermore, the numerical simulations provide an indication of the wealth of patterns that the system can exhibit and the two-dimensional Fourier transform by the image processing interface of GUI from Matlab enables us to gain intensive understanding of these patterns. Besides, the interesting patterns including labyrinthine-like patterns are also numerically observed. All the results obtained reveal the mechanism of morphogenetic processes in adult mesenchymal cells. The patterns obtained corresponding to the patterns induced by morphogens in the vascular mesenchymal cells may play a role in atherosclerotic vascular calcification. (C) 2017 Elsevier Inc. All rights reserved.
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