Control of spiral-wave dynamics in active media by periodic modulation of excitability

Steinbock, Oliver; Zykov, V. S.; Müller, Stefan

doi:10.1038/366322a0

Cited by 307 publications

(227 citation statements)

References 16 publications

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“…57 In the absence of the polymer gel (i.e., in the BZ solution), this two-variable, photosensitive Oregonator model has been used to successfully explain the observed experimental phenomena in a number of studies. [58][59][60][61] Within this model, F specifically accounts for the additional production of bromide ions that are due to illumination by light of a particular wavelength and F is assumed to be proportional to the light intensity. 57 The above approach allows us to reproduce the experimentally observed suppression of oscillations within BZ gels by visible light.…”

Section: Dynamics Of the Bz Gelsmentioning

confidence: 99%

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

et al. 2013

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Species ranging from single-cell organisms to social insects can undergo auto-chemotaxis, where the entities move towards a chemo-attractant that they themselves emit. Polymer gels undergoing the self-oscillating Belousov-Zhabotinsky (BZ) reaction exhibit autonomous, periodic pulsations, which produce chemical species collectively referred to as the activator. The diffusion of this activator into the surrounding solution affects the dynamic behavior of neighboring BZ gels and hence, the BZ gels not only emit, but also respond to self-generated chemical gradients. This review describes recent experimental and computational studies that reveal how this biomimetic behavior effectively allows neighboring BZ gels to undergo cooperative, self-propelled motion. These distinctive properties of the BZ gels provide a route for creating reconfigurable materials that autonomously communicate with neighboring units and thereby actively participate in constructing the desired structures.

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Section: Dynamics Of the Bz Gelsmentioning

confidence: 99%

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

et al. 2013

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“…Next, we revisit the task to extinguish a spiral wave by controlling its tip dynamics such that the whole pattern moves out of the spatial domain towards the Neumann boundaries [9,21,54]. To this goal, following Ex.…”

Section: Example 2: Optimal and Sparse Optimal Position Controlmentioning

confidence: 99%

“…The feedback signals are obtained from wave activity measured at one or several detector points, along detector lines, or in a spatially extended control domain including global feedback control [8,9,20]. Varying the excitability of the light-sensitive BZ medium by changing the globally applied light intensity forces a spiral wave tip to describe a wide range of hypocycloidal and epicycloidal trajectories [21,22]. Moreover, feedback-mediated control loops have been applied successfully in order to stabilize unstable patterns in experiments, such as unstable traveling wave segments and spots [11].…”

Section: Introductionmentioning

confidence: 99%

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Ryll

Löber

Martens

et al. 2016

Understanding Complex Systems

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Abstract. This work deals with the position control of selected patterns in reactiondiffusion systems. Exemplarily, the Schlögl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.

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“…Müller et al used illumination to create and manipulate the dynamics of spiral waves, including the formation of multi-armed spirals and feedback perturbations that govern spiral drift. 45 Here, we report the emergence of diverse spiral waves in a modified BZ reaction system adopting 1,4-CHD instead of malonic acid sustained in a catalyst-immobilized gel membrane. The use of catalyst-immoblized gel membrane provides several advantages compared to the widely used ferroin loaded cationexchange resin system.…”

Section: +mentioning

confidence: 99%

“…Due to the easy implementation of external perturbation, photosensitive reaction-diffusion media have been employed frequently in an effort to understand the interactions between intrinsic dynamics and external perturbations. [38][39][40][41][42][43][44][45] Among these studies, the photosensitive BZ reaction has been primarily employed as the model system, resulting in the oxidation and bromination of malonic acid by acidic bromate present in a metal catalyst, Ru(bpy)3…”

Section: Introductionmentioning

confidence: 99%

Propagating Spiral Waves Obtained in a Catalyst-Immobilized Gel Membrane by the Belousov-Zhabotinsky Reaction System

Kim¹,

Jo²,

Basavaraja³

et al. 2010

Bulletin of the Korean Chemical Society

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The formation of diverse spiral waves was studied in a polyacrylamide gel membrane with ruthenium(4-vinyl-4'-methyl-2,2'-bipyridine)bis(2,2'-bipyridine)bis(hexafluorophosphate) by a gas-free Belousov-Zhabotinisky (BZ) reaction system containing 1,4-cyclohexanedione (1,4-CHD). The gel membrane was found to be receptive for observing propagating waves since a clearer wave-train is obtained during a long reaction time without any disturbance from the immobilized metal catalyst which can be dissolved into the highly acidic solution of the BZ system. The distinctive waves in the system basically depend on both BrO3  and 1,4-CHD in the initial phase, and are influenced by the intensity of illumination of visible light.

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Control of spiral-wave dynamics in active media by periodic modulation of excitability

Cited by 307 publications

References 16 publications

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

Chemo-responsive, self-oscillating gels that undergo biomimetic communication

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

Propagating Spiral Waves Obtained in a Catalyst-Immobilized Gel Membrane by the Belousov-Zhabotinsky Reaction System

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