Literature DB >> 23729972

Logarithmic Lipschitz norms and diffusion-induced instability.

Zahra Aminzare1, Eduardo D Sontag.   

Abstract

This paper proves that contractive ordinary differential equation systems remain contractive when diffusion is added. Thus, diffusive instabilities, in the sense of the Turing phenomenon, cannot arise for such systems. An important biochemical system is shown to satisfy the required conditions.

Entities:  

Year:  2013        PMID： 23729972      PMCID： PMC3666191          DOI： 10.1016/j.na.2013.01.001

Source DB:  PubMed          Journal:  Nonlinear Anal Theory Methods Appl        ISSN： 0362-546X            Impact factor:   2.064


  13 in total

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Authors:  G C Brown; B N Kholodenko
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2.  Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern.

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3.  Cells navigate with a local-excitation, global-inhibition-biased excitable network.

Authors:  Yuan Xiong; Chuan-Hsiang Huang; Pablo A Iglesias; Peter N Devreotes
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4.  A synthetic multicellular system for programmed pattern formation.

Authors:  Subhayu Basu; Yoram Gerchman; Cynthia H Collins; Frances H Arnold; Ron Weiss
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Review 5.  Cell-signalling dynamics in time and space.

Authors:  Boris N Kholodenko
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6.  Modular design of artificial tissue homeostasis: robust control through synthetic cellular heterogeneity.

Authors:  Miles Miller; Marc Hafner; Eduardo Sontag; Noah Davidsohn; Sairam Subramanian; Priscilla E M Purnick; Douglas Lauffenburger; Ron Weiss
Journal:  PLoS Comput Biol       Date:  2012-07-19       Impact factor: 4.475

7.  Dissipative structure: an explanation and an ecological example.

Authors:  L A Segel; J L Jackson
Journal:  J Theor Biol       Date:  1972-12       Impact factor: 2.691

8.  Generation of biological patterns and form: some physical, mathematical, and logical aspects.

Authors:  A Gierer
Journal:  Prog Biophys Mol Biol       Date:  1981       Impact factor: 3.667

9.  Visualization of a Ran-GTP gradient in interphase and mitotic Xenopus egg extracts.

Authors:  Petr Kalab; Karsten Weis; Rebecca Heald
Journal:  Science       Date:  2002-03-29       Impact factor: 47.728

10.  Global entrainment of transcriptional systems to periodic inputs.

Authors:  Giovanni Russo; Mario di Bernardo; Eduardo D Sontag
Journal:  PLoS Comput Biol       Date:  2010-04-15       Impact factor: 4.475
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