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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Modern perspectives on near-equilibrium analysis of Turing systems
TL;DR: In the nearly seven decades since the publication of Alan Turings work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his propose as mentioned in this paper.
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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
- 01 Jan 2005
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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References
Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation
TL;DR: In this paper, the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins associated with root-hair initiation in the plant cell Arabidopsis thaliana was studied.
Localized states qualitatively change the response of ecosystems to varying conditions and local disturbances
TL;DR: In this article, the response of vegetation dynamics in drylands to oscillating precipitation and local disturbances is studied, and it is shown that large amplitude oscillations of the precipitation rate can lead to a collapse of the vegetation in one range, while in the other range, they result in the convergence to a patterned state with a preferred wavelength.
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Stripe to spot transition in a plant root hair initiation model
TL;DR: A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist, and enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem.
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Origin of finite pulse trains: Homoclinic snaking in excitable media.
TL;DR: A new class of phenomena relevant to spatiotemporal dynamics of excitable media, particularly in chemical and biological systems with multiple activators and inhibitors is revealed, thereby blurring the traditional distinction between oscillatory and excitable systems.
•Dissertation
Dynamics of auxin patterning in plant morphogenesis - A multilevel model study
Verônica A. Grieneisen
- 27 Aug 2009
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