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Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

Published online by Cambridge University Press:  22 December 2014

DEBORAH LACITIGNOLA ,
BENEDETTO BOZZINI  and
IVONNE SGURA
DEBORAH LACITIGNOLA
Affiliation:
Dipartimento di Ingegneria Elettrica e dell'Informazione, Università di Cassino e del Lazio Meridionale, Via di Biasio, I-03043 Cassino, Italy email: [email protected]
BENEDETTO BOZZINI
Affiliation:
Dipartimento di Ingegneria dell'Innovazione, Università del Salento, via Monteroni, I-73100 Lecce, Italy email: [email protected]
IVONNE SGURA
Affiliation:
Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, via per Arnesano, I-73100 Lecce, Italy email: [email protected]
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Abstract

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In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013J. Solid State Electr.17, 467–479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, spatially uniform dynamics is discussed and the occurrence of a supercritical Hopf bifurcation for the local kinetics is proved. In the spatial case, initiation of morphological patterns induced by diffusion is shown to occur in a suitable region of the parameter space. The intriguing interplay between Hopf and Turing instability is also considered, by investigating the spatio-temporal behaviour of the system in the neighbourhood of the codimension-two Turing--Hopf bifurcation point. An ADI (Alternating Direction Implicit) scheme based on high-order finite differences in space is applied to obtain numerical approximations of Turing patterns at the steady state and for the simulation of the oscillating Turing–Hopf dynamics.

Keywords

Reaction-diffusion modelsPattern formationTuring-Hopf instabilityADI methodFinite differences
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 2 , April 2015 , pp. 143 - 173
Copyright
Copyright © Cambridge University Press 2014 

References

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