Breathing instability versus drift instability in a two-component reaction-diffusion system

2011 ◽  
Vol 83 (1) ◽  
Author(s):  
Mitsusuke Tarama ◽  
Takao Ohta ◽  
Len M. Pismen
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Two Component ◽  
Drift Instability

scholarly journals Pattern formation in a two-component reaction–diffusion system with delayed processes on a network

2016 ◽  
Vol 462 ◽  
pp. 230-249 ◽  
Author(s):  
Julien Petit ◽  
Malbor Asllani ◽  
Duccio Fanelli ◽  
Ben Lauwens ◽  
Timoteo Carletti
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Two Component

scholarly journals Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Jina Li ◽  
Xuehui Ji
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Reaction Diffusion ◽  
Symmetry Reduction ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Symmetry Classification ◽  
Two Component

In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.

scholarly journals Motion of a Spot in a Reaction Diffusion System under the Influence of Chemotaxis

2018 ◽  
Vol 2018 ◽  
pp. 1-24
Author(s):  
Satoshi Kawaguchi
Keyword(s):  
Reaction Diffusion ◽  
Equation Of Motion ◽  
Circular Motion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Coupling Term ◽  
Two Component ◽  
Global Coupling ◽  
Time Evolution Equation ◽  
Critical Intensity

We consider the motion of a spot under the influence of chemotaxis. We propose a two-component reaction diffusion system with a global coupling term and a Keller-Segel type chemotaxis term. For the system, we derive the equation of motion of the spot and the time evolution equation of the tensors. We show the existence of an upper limit for the velocity and a critical intensity for the chemotaxis, over which there is no circular motion. The chemotaxis suppresses the range of velocity for the circular motion. This braking effect on velocity originates from the refractory period behind the rear interface of the spot and the negative chemotactic velocity. The physical interpretation of the results and its plausibility are discussed.

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

scholarly journals The human EDAR 370V/A polymorphism affects tooth root morphology potentially through the modification of a reaction–diffusion system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Keiichi Kataoka ◽  
Hironori Fujita ◽  
Mutsumi Isa ◽  
Shimpei Gotoh ◽  
Akira Arasaki ◽  
...  
Keyword(s):  
Molecular Mechanisms ◽  
Computational Study ◽  
Reaction Diffusion ◽  
Human Migration ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Tooth Root ◽  
Computed Tomography Images ◽  
Diffusion Dynamics ◽  
Root Morphogenesis

AbstractMorphological variations in human teeth have long been recognized and, in particular, the spatial and temporal distribution of two patterns of dental features in Asia, i.e., Sinodonty and Sundadonty, have contributed to our understanding of the human migration history. However, the molecular mechanisms underlying such dental variations have not yet been completely elucidated. Recent studies have clarified that a nonsynonymous variant in the ectodysplasin A receptor gene (EDAR370V/A; rs3827760) contributes to crown traits related to Sinodonty. In this study, we examined the association between theEDARpolymorphism and tooth root traits by using computed tomography images and identified that the effects of theEDARvariant on the number and shape of roots differed depending on the tooth type. In addition, to better understand tooth root morphogenesis, a computational analysis for patterns of tooth roots was performed, assuming a reaction–diffusion system. The computational study suggested that the complicated effects of theEDARpolymorphism could be explained when it is considered that EDAR modifies the syntheses of multiple related molecules working in the reaction–diffusion dynamics. In this study, we shed light on the molecular mechanisms of tooth root morphogenesis, which are less understood in comparison to those of tooth crown morphogenesis.

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