A new dimension to Turing patterns

T. Leppänen; M.E.J. Karttunen; K. Kaski; R.A. Barrio; L. Zhang

doi:10.1016/S0167-2789(02)00493-1

A new dimension to Turing patterns

T. Leppänen, M.E.J. Karttunen, K. Kaski, R.A. Barrio, L. Zhang

Research output: Contribution to journal › Article › Academic › peer-review

30 Citations (Scopus)

Abstract

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. Keywords: Pattern formation; Reaction–diffusion system; Mathematical biology

Original language	English
Pages (from-to)	35-44
Journal	Physica D: Nonlinear Phenomena
Volume	168-169
DOIs	https://doi.org/10.1016/S0167-2789(02)00493-1
Publication status	Published - 2002

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title = "A new dimension to Turing patterns",

abstract = "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. Keywords: Pattern formation; Reaction–diffusion system; Mathematical biology",

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T1 - A new dimension to Turing patterns

AU - Leppänen, T.

AU - Karttunen, M.E.J.

AU - Kaski, K.

AU - Barrio, R.A.

AU - Zhang, L.

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. Keywords: Pattern formation; Reaction–diffusion system; Mathematical biology

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. Keywords: Pattern formation; Reaction–diffusion system; Mathematical biology

U2 - 10.1016/S0167-2789(02)00493-1

DO - 10.1016/S0167-2789(02)00493-1

M3 - Article

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VL - 168-169

SP - 35

EP - 44

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

ER -

A new dimension to Turing patterns

Abstract

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