Breathing current domains in globally coupled electrochemical systems: A comparison with a semiconductor model

Abstract

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.

Dynamics of hot zones on top of packed-bed reactors

“…The three qualitatively different spatio-temporal patterns (breathing, antiphase and hopping) observed on the top of the packed-bed reactor look strikingly similar to those experimentally observed in 2-D domains in electrochemical field (Hudson et al, 1993;Plenge et al, 2001;Birzu et al, 2003;Lee et al, 2003). Birzu et al (2003) concluded that the evolution of these spatio-temporal patterns during electrodissolution of a metal disk electrode was caused by the presence of (negative) global coupling.…”

Swing, release, and escape mechanisms contribute to the generation of phase-locked cluster patterns in a globally coupled FitzHugh-Nagumo model

“…Globally coupled oscillatory systems have been studied both experimentally and theoretically in a variety of systems including chemical reactions [10,11,12,13,14,15], metabolic oscillators [16,17], electrochemical oscillators [18,19,20,21,22,23,24,25,26,27,28], catalytic reactions [29], neuronal networks [5,30,31,32,33,34,35], salt-water oscillators [36], laser arrays [37], and cardiac oscillators [38,39]. Theoretical studies have been performed using activator-inhibitor type models that explicitely describe the dynamics of the participating physical (chemical, biological, etc) variables.…”

Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection

“…Global feedback (a closed-loop control, as opposed to open-loop control or external forcing) has been shown to generate a variety of patterns, including cluster states in oscillatory active media [10]. Experimental and theoretical studies in the CO oxidation on platinum surfaces [11][12][13][14][15][16] and other catalytic processes [17,18], as well as in electrochemistry [19] or in semiconductors [20,21], have shown that global feedback can be employed to control propagating waves and to generate spatially periodic patterns such as Turing patterns or traveling waves (for a review see [22]). …”