Spatiotemporal complexity in a diffusive Brusselator model

2021 ◽  
Author(s):  
Xiaoxue Fu ◽  
Ranchao Wu ◽  
Mengxin Chen ◽  
Hongxia Liu
Keyword(s):  
Brusselator Model

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 Stationary localized structures and the effect of the delayed feedback in the Brusselator model

2018 ◽  
Vol 376 (2135) ◽  
pp. 20170385 ◽  
Author(s):  
B. Kostet ◽  
M. Tlidi ◽  
F. Tabbert ◽  
T. Frohoff-Hülsmann ◽  
S. V. Gurevich ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Dissipative Structures ◽  
Delayed Feedback ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Delayed Feedback Control ◽  
Brusselator Model ◽  
Localized Structures ◽  
Reaction Diffusion Model ◽  
Spatial Dimensions

The Brusselator reaction–diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce a spontaneous motion of both localized and periodic dissipative structures. We characterize this motion by estimating the threshold and the velocity of the moving dissipative structures. This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)’.

scholarly journals Regional Green Development and Spatial Evolution in China: Abiding by Theory of Dissipative Structure

2018 ◽  
Vol 53 ◽  
pp. 04008
Author(s):  
Fumin Deng ◽  
Hui Zhu ◽  
Xuedong Liang
Keyword(s):  
Economic Development ◽  
Dissipative Structure ◽  
Eastern China ◽  
Indicator System ◽  
Entropy Method ◽  
Central China ◽  
Western China ◽  
Brusselator Model ◽  
Energy Factors ◽  
Green Development

Regional green development can commendably abide by the theory of dissipative structure. The relative dissipative characteristics taken on by regional development are analyzed, in which the energy factors and resources factors are incorporated into the green economic development and green environment support subsystems (2GE system) in line with the definite input characteristics. A more representative indicator system is established, with positive and negative entropy indexes involved. As Brusselator model and information entropy method are employed to calculate the data of 30 China’s provinces from 2008 to 2015, the findings bespeak that green development in China lays particular stress on green economic development assuming higher environment pressure and cost. The development among various regions is getting progressively and evidently different, which is manifested as potent economic base and abundant natural resources in the Eastern China; the backward green economic development and the progress of green environment in Central China; the pursuit of green economic development at the expense of the green environment in Western China and Northeastern China.

scholarly journals Internet Public Opinion Diffusion Mechanism in Public Health Emergencies: Based on Entropy Flow Analysis and Dissipative Structure Determination

2021 ◽  
Vol 9 ◽  
Author(s):  
Wanlian Li ◽  
Feng Zeng ◽  
Wei Zhou ◽  
Zhishao Chen
Keyword(s):  
Public Health ◽  
Public Opinion ◽  
Dissipative Structure ◽  
Trigger Point ◽  
Diffusion Mechanism ◽  
Flow Analysis ◽  
Entropy Method ◽  
Entropy Flow ◽  
Brusselator Model ◽  
The Government

As an empirical case, this study selected the illegal production process incidents of rabies and DPT (Diphtheria, Pertussis, Tetanus) vaccines by Changchun Longevity Biotechnology Co., Ltd., which occurred in July 2018. Based on the four factors involved in the spread of public opinion, the public health emergency, netizen, network media, and government, Brusselator model, and entropy method were applied to calculate the positive and negative entropy—to verify whether the Internet public opinion system is a dissipative structure. This study verified four evolution mechanisms in Internet public opinion diffusion, among which the trigger point of entropy-control occurred in the germination mechanism, the entropy-controlled disposal point occurred in the outbreak and fluctuating mechanism, and then became latency in the elimination mechanism. It provides a theoretical reference for the government to judge the stage of such diffusion and improve the governance ability of the opinion mentioned above.

scholarly journals Particle in the Brusselator model with flow

2002 ◽  
Vol 163 (1-2) ◽  
pp. 80-88 ◽  
Author(s):  
P.V Kuptsov ◽  
S.P Kuznetsov ◽  
E Mosekilde
Keyword(s):  
Brusselator Model

PATTERN FORMATION IN SMALL ARRAYS OF LOCALLY COUPLED OSCILLATORS

2005 ◽  
Vol 15 (07) ◽  
pp. 2283-2293 ◽  
Author(s):  
REBECCA ELLISON ◽  
VIRGINIA GARDNER ◽  
JOEL LEPAK ◽  
MEGHAN O'MALLEY ◽  
JOSEPH PAULLET ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Landau Equation ◽  
Current Model ◽  
Relaxation Oscillation ◽  
Chaotic Regime ◽  
Phase Oscillators ◽  
Ginzburg Landau ◽  
Brusselator Model ◽  
Small Domain ◽  
Oscillatory Media

We investigate small two-dimensional arrays of locally coupled phase oscillators which are shown to exhibit a surprising variety of stable structures which include: single spiral waves, spiral pairs and spirals with secondary periodic core motion. This periodic core motion is not the core meander familiar to many models of active media, but is in fact induced by the boundary of the small domain. Such boundary motion was investigated by Sepulchre and Babloyantz [1993] for the complex Ginzburg–Landau equation and for the Brusselator model in a relaxation oscillation parameter regime. The current model confirms the findings in [Sepulchre & Babloyantz, 1993] and sheds new light on the origin of such motion. The model also exhibits other patterns, as well as a chaotic regime. We discuss the transition between patterns as the form of the coupling is changed as well as implications for pattern formation in general oscillatory media.

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