Turing bifurcation in a reaction–diffusion system with density-dependent dispersal

2010 ◽  
Vol 389 (9) ◽  
pp. 1812-1818 ◽  
Author(s):  
Niraj Kumar ◽  
Werner Horsthemke
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Density Dependent ◽  
Turing Bifurcation ◽  
Density Dependent Dispersal

scholarly journals Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Qianiqian Zheng ◽  
Zhijie Wang ◽  
Jianwei Shen ◽  
Hussain Muhammad Ather Iqbal
Keyword(s):  
Pattern Formation ◽  
Local Equilibrium ◽  
Reaction Diffusion ◽  
Taylor Series Expansion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Bifurcation ◽  
Noise Function ◽  
Pattern Formations ◽  
Stochastic Reaction

Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS), Stochastic Reaction-Diffusion System (SRDS) is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.

Turing bifurcation analysis for a predator-prey reaction-diffusion system

2017 ◽  
Vol 132 (9) ◽  
Author(s):  
Memoona Mehboob ◽  
Salman Ahmad ◽  
Muhammad Aqeel ◽  
Faizan Ahmed ◽  
Asad Ali
Keyword(s):  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Predator Prey ◽  
Turing Bifurcation

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.

Geographic tongue as a reaction–diffusion system

2021 ◽  
Vol 31 (3) ◽  
pp. 033118
Author(s):  
Margaret K. McGuire ◽  
Chase A. Fuller ◽  
John F. Lindner ◽  
Niklas Manz
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System
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