Journal Article10.1016/J.PHYSD.2020.132735
Bistability, wave pinning and localisation in natural reaction–diffusion systems
Alan R Champneys,Fahad Al Saadi,Victor F. Breña–Medina,Verônica A. Grieneisen,Athanasius F. M. Marée,Nicolas Verschueren,Nicolas Verschueren,Nicolas Verschueren,Bert Wuyts,Bert Wuyts +9 more
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TL;DR: In this paper, a synthesis of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction-diffusion equations is presented.
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About: This article is published in Physica D: Nonlinear Phenomena. The article was published on 01 Feb 2021. The article focuses on the topics: Cellular polarity & Reaction–diffusion system.
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Citations
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Stability of spatially periodic pulse patterns in a class of singularly perturbed reaction-diffusion equations
H. van dePloeg,Arjen Doelman +1 more
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TL;DR: In this paper, a stability theory for spatially periodic patterns on R was developed for a class of singularly perturbed reaction-diffusion equations that can be represented by the generalized Gierer-Meinhardt equations as "normal form".
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Spots, stripes, and spiral waves in models for static and motile cells : GTPase patterns in cells.
TL;DR: In this article, the wave-pinning model for GTPase-induced cell polarization is revisited, together with a number of extensions proposed in the literature, including the introduction of sources and sinks of active and inactive GTPases, and negative feedback from F-actin to gTPase activity.
Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems
TL;DR: In this paper, the authors considered a general class of models with simple cubic autocatalytic nonlinearity and arbitrary constant and linear kinetics, including Schnakenberg and Brusselator models.
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•Posted Content
Spots, strips, and spiral waves in models for static and motile cells
TL;DR: The wave-pinning model for GTPase-induced cell polarization is revisited, together with a number of extensions proposed in the literature, and the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.
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Mechanisms behind the puzzle: microtubule–microfilament cross-talk in pavement cell formationThis review is one of a selection of papers published in the Special Issue on Plant Cell Biology.
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Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches
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Turning ON the switch – RhoGEFs in plants
Keren Shichrur,Shaul Yalovsky +1 more
TL;DR: Alfred Wittinghofer and co-workers' description of a group of plant-specific RhoGEFs opens the way for the elucidation of ROP signaling cascades from membrane receptors to responses.
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Assessing the robustness of spatial pattern sequences in a dryland vegetation model
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