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.

ASYMPTOTIC EQUIVALENCE OF A REACTION-DIFFUSION SYSTEM TO THE CORRESPONDING SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

1995 ◽  
Vol 05 (06) ◽  
pp. 813-834 ◽  
Author(s):  
HIROKI HOSHINO ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Energy Method ◽  
Large Time ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior ◽  
Asymptotic Equivalence

Large time behavior of the solution to some simple reaction-diffusion system is studied. It is proved that the solution behaves like the solution to the corresponding system of ordinary differential equations as time goes to infinity. The proof is based on an energy method combined with the Lp−Lqestimate for the associated semigroup.

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

Bone Formation Based on the Turing Model under Compressed Loading Condition

2008 ◽  
Vol 33-37 ◽  
pp. 1011-1016 ◽  
Author(s):  
Li Hua Jia ◽  
Mamtimin Gheni ◽  
Hazirti Eli ◽  
Xamxinur Abdikerem ◽  
Masanori Kikuchi
Keyword(s):  
Numerical Simulation ◽  
Bone Formation ◽  
Bone Mass ◽  
Loading Condition ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Forming Process ◽  
Bone Model ◽  
Initial Load

In this paper, the iBone (Imitation Bone) model which is coupled with Turing reaction-diffusion system and FEM, is used. The numerical simulation of bone forming process by considering the osteoclasts and osteoblasts process are conducted. The results shown, that the bone mass is increased with increase of the initial load value, then fibula and femur bones are obtained respectively by keeping the required bone forming value. The different bone shapes are obtained by changing the both bone keeping value and the compressing force value. When set larger bone keeping value by keeping larger constant compressing force value, bone shape as a pipe with hole just like femur, when set smaller bone keeping value by keeping the smaller constant compressing force value, it is close to solid pillar as like fibula.

scholarly journals Stability analysis for Selkov-Schnakenberg reaction-diffusion system

2021 ◽  
Vol 19 (1) ◽  
pp. 46-62
Author(s):  
Khaled Al Noufaey
Keyword(s):  
Differential Equations ◽  
Diffusion Coefficients ◽  
Reaction Diffusion ◽  
Oscillatory Solution ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
System Stability ◽  
Hopf Bifurcation Point ◽  
The Galerkin Method ◽  
Diagram Analysis

Abstract This study provides semi-analytical solutions to the Selkov-Schnakenberg reaction-diffusion system. The Galerkin method is applied to approximate the system of partial differential equations by a system of ordinary differential equations. The steady states of the system and the limit cycle solutions are delineated using bifurcation diagram analysis. The influence of the diffusion coefficients as they change, on the system stability is examined. Near the Hopf bifurcation point, the asymptotic analysis is developed for the oscillatory solution. The semi-analytical model solutions agree accurately with the numerical results.

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