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  Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

Vidal-Henriquez, E., Zykov, V. S., Bodenschatz, E., & Gholami, A. (2017). Convective instability and boundary driven oscillations in a reaction-diffusion-advection model. Chaos, 27(10): 103110. doi:10.1063/1.4986153.

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Vidal-Henriquez, Estefania1, Author              
Zykov, Vladimir S.1, Author              
Bodenschatz, Eberhard1, Author              
Gholami, Azam1, Author              
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1Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063287              

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 Abstract: In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

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Language(s): eng - English
 Dates: 2017-10-092017-10
 Publication Status: Published in print
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 Rev. Type: Peer
 Identifiers: DOI: 10.1063/1.4986153
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Title: Chaos
Source Genre: Journal
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Pages: 10 Volume / Issue: 27 (10) Sequence Number: 103110 Start / End Page: - Identifier: -