Numerical simulation to study the pattern formation of reaction–diffusion Brusselator model arising in triple collision and enzymatic

2018 ◽  
Vol 56 (6) ◽  
pp. 1543-1566 ◽  
Author(s):  
Aisha M. Alqahtani
Keyword(s):  
Numerical Simulation ◽  
Pattern Formation ◽  
Reaction Diffusion ◽  
Triple Collision ◽  
Brusselator Model

scholarly journals Pattern formation in reaction–diffusion system on membrane with mechanochemical feedback

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Naoki Tamemoto ◽  
Hiroshi Noguchi
Keyword(s):  
Pattern Formation ◽  
Plasma Membranes ◽  
Reaction Diffusion ◽  
Living Cells ◽  
Nonequilibrium Dynamics ◽  
Membrane Deformation ◽  
Brusselator Model ◽  
Diffusion Dynamics ◽  
Curved Membranes ◽  
Membrane Shape

Abstract Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction–diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.

scholarly journals Spatio-temporal Brusselator Model and Biological Pattern Formation

2021 ◽  
pp. 88-99
Author(s):  
Zakir Hossine ◽  
Oishi Khanam ◽  
Md. Mashih Ibn Yasin Adan ◽  
Md. Kamrujjaman
Keyword(s):  
Pattern Formation ◽  
Diffusion Model ◽  
Initial Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Brusselator Model ◽  
Reaction Diffusion Model ◽  
Biological Pattern Formation ◽  
Spatio Temporal

This paper explores a two-species non-homogeneous reaction-diffusion model for the study of pattern formation with the Brusselator model. We scrutinize the pattern formation with initial conditions and Neumann boundary conditions in a spatially heterogeneous environment. In the whole investigation, we assume the case for random diffusion strategy. The dynamics of model behaviors show that the nature of pattern formation with varying parameters and initial conditions thoroughly. The model also studies in the absence of diffusion terms. The theoretical and numerical observations explain pattern formation using the reaction-diffusion model in both one and two dimensions.

scholarly journals Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Hua Liu ◽  
Yong Ye ◽  
Yumei Wei ◽  
Weiyuan Ma ◽  
Ming Ma ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Pattern Formation ◽  
Allee Effect ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Point Of View ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pattern Formations

In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations.

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.

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