Spiral Instabilities in a Reaction Diffusion System

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4072-4085
Author(s):  
Lu-Qun Zhou ◽  
Chun-Xian Zhang ◽  
Qi Ouyang
Keyword(s):  
Phase Diagram ◽  
Experimental Studies ◽  
Reaction Diffusion ◽  
Theoretical Explanation ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Bz Reaction ◽  
Long Wavelength ◽  
Spiral Dynamics ◽  
Chemical Turbulence

A series of experimental studies on spiral dynamics and instabilities in a spatial open reactor with the Belousov-zhabotinsky (BZ) reaction are reported. We present a phase diagram showing different spiral dynamic regimes. Two types of spiral instabilities, the Doppler instability and the long wavelength instability, are observed in the experiments. All these instabilities lead to a state of spatiotemporal chaos or chemical turbulence. Theoretical explanation are given for each instability.

Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Characterization

Bifurcation Analysis and Spatiotemporal Patterns in a Diffusive Predator–Prey Model

2014 ◽  
Vol 24 (06) ◽  
pp. 1450081 ◽  
Author(s):  
Guangping Hu ◽  
Xiaoling Li ◽  
Shiping Lu ◽  
Yuepeng Wang
Keyword(s):  
Pattern Formation ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Target Pattern ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

In this paper, we consider a species predator–prey model given a reaction–diffusion system. It incorporates the Holling type II functional response and a quadratic intra-predator interaction term. We focus on the qualitative analysis, bifurcation mechanisms and pattern formation. We present the results of numerical experiments in two space dimensions and illustrate the impact of the diffusion on the Turing pattern formation. For this diffusion system, we also observe non-Turing structures such as spiral wave, target pattern and spatiotemporal chaos resulting from the time evolution of these structures.

Control of spiral instabilities in reaction-diffusion systems

2005 ◽  
Vol 77 (8) ◽  
pp. 1395-1408 ◽  
Author(s):  
Hui-Min Liao ◽  
Min-Xi Jiang ◽  
Xiao-Nan Wang ◽  
Lu-Qun Zhou ◽  
Qi Ouyang
Keyword(s):  
Traveling Waves ◽  
Reaction Diffusion ◽  
Oscillatory System ◽  
Local Area ◽  
Spatiotemporal Chaos ◽  
Oscillatory Regime ◽  
Reaction Diffusion Systems ◽  
Long Wavelength ◽  
Diffusion Systems ◽  
Belousov Zhabotinsky Reaction

Spiral instabilities and their controls are investigated in a reaction-diffusion system using the Belousov-Zhabotinsky reaction. Two spiral instabilities, the long-wavelength instability and the Doppler instability, are reported, which can lead to spatiotemporal chaos. The long-wavelength instability occurs in an oscillatory regime, while the Doppler instability occurs in an excitable regime. To control these two instabilities, two different strategies are proposed according to their defect-generating mechanisms. For the long-wavelength instability in an oscillatory system, the control can be achieved by introducing a local pacemaker, which emits stable traveling waves to sweep off the unstable spiral defects. For the Doppler instability, the control can be achieved by trapping the spiral tip with a local area of higher diffusion coefficient than its surroundings.

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