TY - JOUR
T1 - A new dimension to Turing patterns
AU - Leppänen, Teemu
AU - Karttunen, Mikko
AU - Kaski, Kimmo
AU - Barrio, R.A.
AU - Zhang, Limei
PY - 2002
Y1 - 2002
N2 - It is well known that simple reaction-diffusion systems can display very rich pattern formation behaviour. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signalling mechanism for neuronal growth. (C) 2002 Elsevier Science B.V. All rights reserved.
AB - It is well known that simple reaction-diffusion systems can display very rich pattern formation behaviour. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic Turing system in three dimensions and then the well-known Gray-Scott model. In the latter case, we added a small number of morphogen sources in the system in order to study its robustness and the formation of connections between the sources. Our results raise the question of whether Turing patterning can produce an inductive signalling mechanism for neuronal growth. (C) 2002 Elsevier Science B.V. All rights reserved.
KW - mathematical biology
KW - pattern formation
KW - reaction-diffusion systemMathematical biology; Pattern formation; Reaction-diffusion system
U2 - 10.1016/S0167-2789(02)00493-1
DO - 10.1016/S0167-2789(02)00493-1
M3 - Article
SN - 0167-2789
VL - 168-169
SP - 35
EP - 44
JO - PHYSICA D: NONLINEAR PHENOMENA
JF - PHYSICA D: NONLINEAR PHENOMENA
M1 - PII S0167-2789(02)00493-1
ER -