Tuning the range of spatial coupling in electrochemical systems: From local via nonlocal to global coupling

Mazouz, Nadia; Flätgen, Georg; Krischer, Katharina

doi:10.1103/physreve.55.2260

Cited by 92 publications

(82 citation statements)

References 34 publications

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“…Characteristic examples pertain to neuroscience [11,12], chemical oscillators [13,14], electrochemical systems [15], and Josephson junctions [16]. A new impulse to study such networks was given, in particular, by the discovery of so-called chimera states [17,18].…”

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confidence: 99%

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

et al. 2011

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We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous Rössler systems reveal that intermediate, partially coherent states represent characteristic spatiotemporal patterns at the transition from coherence to incoherence. Understanding the dynamics on networks is at the heart of modern nonlinear science and has a wide applicability to various fields [1,2]. Thus, network science is a vibrant, interdisciplinary research area with strong connections to physics. For example, concepts of theoretical physics like the Turing instability, which is a known paradigm of non-equilibrium self-organization in spacecontinuous systems, have recently been transferred to complex networks [3]. While spatially extended systems show pattern formation mediated by diffusion, i.e., local interactions, a network takes also into account long-range and global interactions yielding more realistic spatial geometries.Network topologies like all-to-all coupling of, for instance, phase oscillators (Kuramoto model) or chaotic maps (Kaneko model) were intensively studied , and numerous characteristic regimes were found [4][5][6]. In particular, for globally coupled chaotic maps they rangefor decreasing coupling strength -from complete chaotic synchronization via clustering and chaotic itineracy to complete desynchronization. The opposite case, i.e., nearest-neighbor coupling, is known as lattice dynamical systems of time-continuous oscillators, or coupled map lattices if the oscillator dynamics is discrete in time. These kinds of networks arise naturally as discrete approximation of systems with diffusion and have also been thoroughly studied. They can demonstrate rich dynamics such as solitons, kinks, etc. up to fully developed spatiotemporal chaos [6][7][8][9][10].The case of networks with nonlocal coupling, however, has been much less studied in spite of numerous applications in different fields. Characteristic examples pertain to neuroscience [11,12], chemical oscillators [13,14], electrochemical systems [15], and Josephson junctions [16]. A new impulse to study such networks was given, in particular, by the discovery of so-called chimera states [17,18]. The main peculiarity of these spatio-temporal patterns is that they have a hybrid spatial structure, partially coherent and partially incoherent, which can develop in networks of identical oscillators without any sign of inhomogeneity.In this Letter we discuss the transition between coherent and incoherent dynamics in networks of nonlocally coupled oscillators. We start with coupled chaotic mapswhere z i are real dynamic variables (i = 1, ..., N , N 1 and the inde...

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Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

et al. 2011

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“…Moreover, Eq. (1) predicts a peculiar property of spatial coupling in electrochemical systems, namely, that its range, i.e., the distance over which a perturbation at a given point is felt instantaneously and with a finite strength, increases with the distance between the WE and the CE [14]. This is reflected in the dependence of Eq.…”

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“…The last term of Eq. (1) describes the nonlocal migration coupling, which is mediated through the electric potential in the electrolyte, x; z, obtained by solving Laplace's equation [14,15] (x and z being the coordinates parallel and perpendicular to the electrode, respectively, and z WE a position at the WE; is the dimensionless conductivity). Moreover, Eq.…”

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Transitions to Electrochemical Turbulence

et al. 2005

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We report experimental evidence of transitions from limit cycle oscillations through a phase turbulent regime to space-time defect turbulence in a spatially (quasi-)one-dimensional electrochemical system with nonlocal coupling. The transitions are characterized in terms of the defect density, the KarhunenLoève decomposition dimension, and a measure of the degree of spatial correlation in the data. Furthermore, these quantities give the first experimental confirmation that the spatial coupling range in electrochemical systems indeed depends on the distance between the working and the counterelectrode.

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“…A class of systems with intrinsic nonlocal coupling are electrochemical systems [14,15]. In a previous paper [16], some of us reported novel types of experimentally observed patterns arising during an electrochemical reaction, however, without being able to explain the origin of the unusual dynamics.…”

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Asymmetric Target Patterns in One-Dimensional Oscillatory Media with Genuine Nonlocal Coupling

2005

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We report the observation of a self-organized asymmetric wave source in a one-dimensional (1D) electrochemical system, namely, the hydrogen oxidation reaction on Pt in the presence of poisons. Numerical simulations reveal that the nonlocal migration coupling is crucial for the endogenous persistence of the perturbation that causes the asymmetry. Experiments and simulations agree perfectly for the regular and irregular variant of these asymmetric waves, manifesting the existence of nonlocal coupling induced patterns also in physical systems.

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Tuning the range of spatial coupling in electrochemical systems: From local via nonlocal to global coupling

Cited by 92 publications

References 34 publications

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

Loss of Coherence in Dynamical Networks: Spatial Chaos and Chimera States

Transitions to Electrochemical Turbulence

Asymmetric Target Patterns in One-Dimensional Oscillatory Media with Genuine Nonlocal Coupling

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