Amplitude equations for breathing spiral waves in a forced reaction-diffusion system

2011 ◽  
Vol 135 (10) ◽  
pp. 104112 ◽  
Author(s):  
Pushpita Ghosh ◽  
Deb Shankar Ray
Keyword(s):  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Amplitude Equations

Inducing and modulating spiral waves by delayed feedback in a uniform oscillatory reaction–diffusion system

2010 ◽  
Vol 371 (1-3) ◽  
pp. 60-65 ◽  
Author(s):  
Haixiang Hu ◽  
Xiaochun Li ◽  
Zhiming Fang ◽  
Xu Fu ◽  
Lin Ji ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Delayed Feedback ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Oscillatory Reaction

SPIRAL WAVE MAINTAINED BY NOISE

2004 ◽  
Vol 04 (03) ◽  
pp. L447-452 ◽  
Author(s):  
AI ZHONG LEI ◽  
QIAN SHU LI ◽  
WEIGUO XU ◽  
DAIPING HU
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Noise Level ◽  
Gaussian White Noise ◽  
Spiral Wave ◽  
Reaction Diffusion ◽  
Spiral Waves ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Zero Level

The effect of Gaussian white noise on a chemical wavefront is studied in a modified FitzHugn–Nagumo model by applying numerical simulations. A rotating spiral waves can be formed if the medium is excitable enough and the fronts has a free end, when the reaction diffusion system is disturbed by a certain non-zero level noise. It is counterintuitive that noise plays a constructive role in the product and propagation of single spiral waves in this letter. Weak or strong noise will make against the product and propagation of spiral waves. In a certain noise level, spiral wave can be maintained in a medium, where such spiral waves cannot be observed in the absence of the noise.

Derivation of the Amplitude Equation for Reaction–Diffusion Systems via Computer-Aided Multiple-Scale Expansion

2014 ◽  
Vol 24 (07) ◽  
pp. 1450101 ◽  
Author(s):  
Kaier Wang ◽  
Moira L. Steyn-Ross ◽  
D. Alistair Steyn-Ross ◽  
Marcus T. Wilson
Keyword(s):  
Reaction Diffusion ◽  
Multiple Scale ◽  
Research Literature ◽  
Amplitude Equation ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reduced Form ◽  
Amplitude Equations ◽  
Reaction Diffusion Systems ◽  
Scale Expansion

The amplitude equation describes a reduced form of a reaction–diffusion system, yet still retains its essential dynamical features. By approximating the analytic solution, the amplitude equation allows the examination of mode instability when the system is near a bifurcation point. Multiple-scale expansion (MSE) offers a straightforward way to systematically derive the amplitude equations. The method expresses the single independent variable as an asymptotic power series consisting of newly introduced independent variables with differing time and space scales. The amplitude equations are then formulated under the solvability conditions which remove secular terms. To our knowledge, there is little information in the research literature that explains how the exhaustive workflow of MSE is applied to a reaction–diffusion system. In this paper, detailed mathematical operations underpinning the MSE are elucidated, and the practical ways of encoding these operations using MAPLE are discussed. A semi-automated MSE computer algorithm Amp_solving is presented for deriving the amplitude equations in this research. Amp_solving has been applied to the classical Brusselator model for the derivation of amplitude equations when the system is in the vicinity of a Turing codimension-1 and a Turing–Hopf codimension-2 bifurcation points. Full open-source Amp_solving codes for the derivation are comprehensively demonstrated and available to the public domain.

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