Erratum: Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable media [CHAOS 1, 303–334 (1991)]

1992 ◽  
Vol 2 (2) ◽  
pp. 273-273 ◽  
Author(s):  
Arthur T. Winfree
Keyword(s):  
Spiral Wave ◽  
Excitable Media

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media

2021 ◽  
Vol 31 (5) ◽  
pp. 053131
Author(s):  
Karthikeyan Rajagopal ◽  
Shaobo He ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Spiral Wave ◽  
Wave Formation ◽  
Excitable Media

scholarly journals Spiral Wave Formation in Three-Dimensional Excitable Media

1996 ◽  
Vol 77 (15) ◽  
pp. 3244-3247 ◽  
Author(s):  
Takashi Amemiya ◽  
Sándor Kádár ◽  
Petteri Kettunen ◽  
Kenneth Showalter
Keyword(s):  
Three Dimensional ◽  
Spiral Wave ◽  
Wave Formation ◽  
Excitable Media

scholarly journals Spiral waves within a bistability parameter region of an excitable medium

2022 ◽  
Author(s):  
Vladimir Zykov ◽  
Eberhard Bodenschatz
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Gradient Flow ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Excitable Media ◽  
Circular Trajectory ◽  
Parameter Region ◽  
Scroll Wave

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

scholarly journals Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Rupamanjari Majumder ◽  
Iolanda Feola ◽  
Alexander S Teplenin ◽  
Antoine AF de Vries ◽  
Alexander V Panfilov ◽  
...  
Keyword(s):  
Real Time ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Media ◽  
Wave Dynamics ◽  
Linear Waves ◽  
Cardiac System ◽  
Spatiotemporal Control ◽  
Forced Movement

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.

scholarly journals Effects of randomization of characteristic times on spiral wave generation in a simple cellular automaton model of excitable media

AIP Advances ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 085116
Author(s):  
Vincent Vangelista ◽  
Karl Amjad-Ali ◽  
Minhyeok Kwon ◽  
Paulo H. Acioli
Keyword(s):  
Cellular Automaton ◽  
Spiral Wave ◽  
Wave Generation ◽  
Cellular Automaton Model ◽  
Excitable Media

scholarly journals Spiral waves in excitable media: a model for diverse aspects of organismal development

1992 ◽  
Vol 6 ◽  
pp. 98-98
Author(s):  
Daniel C. Fisher
Keyword(s):  
Spatial Organization ◽  
Full Range ◽  
Phase Relationship ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Media ◽  
Spiral Growth ◽  
Geometrical Properties ◽  
Logarithmic Spirals ◽  
The Common

Conical skeletal elements of various morphologies are a feature common to numerous Lower and Middle Cambrian organisms of problematic affinity, not to mention their occurrence in multiple extant metazoan phyla. In some cases these display helicospiral morphology, sometimes with dextral and sinistral morphs that may have been paired structures in a bilaterally symmetrical body plan. Such paired elements, including spines of coeloscleritophorans, appear to show a spicular substructure with some suggestion of spatial organization comparable to that of phyllotactic systems in vascular plants. These recurring structural themes raise old questions regarding the significance and mode of development of spiral forms and patterns in many organisms, both unicellular and multicellular.Most recent work on phyllotaxis has interpreted patterns of spiral organization as emergent geometrical properties of systems controlled by local reaction-diffusion interactions around the developing plant axis, without recourse to any explicitly spiral process. The term “generative spiral,” for the pattern linking consecutively formed elements, has thus taken on a purely descriptive, rather than mechanistic, meaning. Likewise, helicospiral shells and comparable structures are generally assumed to reflect no truly spiral growth mechanism, but rather, the regular scaling and displacement of a fundamentally concentric, cone-within-cone, accretionary system. Explanations for the common appearance of such forms include the structural strength offered by adherent whorls (though many forms are evolute), and the simplicity of isometric growth (though departures from logarithmic spirals are common).An alternative perspective was suggested initially by discovery of a higher order pattern in the phyllotactic systems of some conifers, wherein the handedness of the generative spiral reverses as each parent axis gives rise to daughters, through the full range of levels in the branching hierarchy. Although this may be explicable in conventional terms, it may also be interpreted as involving a spiral wave of activation passing rhythmically around the plant axis, at or within some critical distance of the apical meristem. Models for such phenomena are provided by several physical systems involving excitable media, the most well known of which is the Belousov-Zhabotinsky reaction, and by some biological systems, such as neural networks or aggregations of slime mold. At nearly the opposite end of the organismic realm, vertebrate teeth, most of which are subtly but fundamentally helicospiral in form, show features that also suggest rotating waves of activity. These include the common presence of an axial canal in the dentin underlying tooth cusps, which could represent the phase singularity of a rotating wave in the layer of odontoblasts responsible for dentin formation, and asymmetries in autoradiographic patterns associated with developing teeth. In such systems it may be generally true that the period of other physiological cycles that modulate secretory activity is not a simple multiple of the period of rotation of the spiral wave. This would result in a regular change in phase relationship, generating helicospiral form. Additional applications of this principle may illumine features as diverse as bovid horns and the handedness of supernumerary appendages in grafting experiments on insects and amphibians. Spiral waves in excitable media also have properties of symmetry and capacity for generating serial structure that make them intriguing candidates for involvement in even earlier stages of metazoan development.

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