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
47
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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
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.
53
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".
43
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.
19
•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.
18
References
Stationary and oscillatory localized patterns in ratio-dependent predator–prey systems
TL;DR: In this article, a simple predator-prey model with rational interaction terms in one and two spatial dimensions is investigated, focusing on a case with linear interaction and saturation, and an analysis for long domains in 1D is undertaken using ideas from spatial dynamics.
9
Probabilistic Foundations of Spatial Mean-field Models in Ecology and Applications
TL;DR: This work demonstrates convergence to a mean-field limit for a general class of stochastic models representing each individual ecological event in the limit of large system size, and provides an accessible general framework for spatially extending many classical finite-state models from ecology and population dynamics.
7
•Posted Content
Probabilistic Foundations of the Staver-Levin Model
Denis D. Patterson,Simon A. Levin,A. Carla Staver,Jonathan Touboul +3 more
- 15 Nov 2019
TL;DR: In this paper, an interacting particle system of vegetation dynamics and show its convergence towards a generalized, spatially extended Staver-Levin model in an appropriate scaling limit is presented.
2
Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations ∗
Arjen Doelman,Tasso J. Kaper +1 more
TL;DR: This article develops a theory for the semistrong interaction of pulses in a class of singularly perturbed coupled reaction-diffusion equations that includes the (generalized) Gierer--Meinhardt, Gray--Scott, Schnakenberg, and Thomas models, among others.
An intracellular partitioning-based framework for tissue cell polarity in plants and animals
Katie Abley,Pierre Barbier de Reuille,Pierre Barbier de Reuille,Pierre Barbier de Reuille,David Strutt,Andrew Bangham,Przemyslaw Prusinkiewicz,Athanasius F. M. Marée,Verônica A. Grieneisen,Enrico Coen +9 more
TL;DR: It is shown how this intracellular partitioning-based framework can be applied to both plant and animal systems, allowing different processes to be placed in a common evolutionary and mechanistic context.