Third generation cellular automaton for modeling excitable media
TLDR
In this article, a cellular automation model of excitable media with improved treatments of diffusion and wave propagation, and slow dynamics of the recovery variable is introduced. But the model is computationally efficient and faithful to the underlying partial differential equations.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1992-03-01 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Excitable medium & Continuous automaton.read more
Citations
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Journal ArticleDOI
Fast Simulations of Waves in Three-Dimensional Excitable Media
TL;DR: A fast numerical scheme based on the model of Barkley is extended to three space dimensions to provide greater accuracy and a 19-point approximation for the Laplacian operator in 3D is shown to have significant advantages over the commonly used 7-point formula.
Journal ArticleDOI
Cellular automata for reaction-diffusion systems
TL;DR: A class of cellular automata for reaction-diffusion systems is presented, based on a local average for the diffusive dynamics, and closely related to finite difference schemes.
Journal ArticleDOI
Convolution—thresholding methods for interface motion
Steven J. Ruuth,Barry Merriman +1 more
TL;DR: The relation of convolution–thresholding schemes to previous methods is summarized, the theoretical and algorithmic development of this approach is reviewed, and recent applications to computer vision, developmental biology, excitable media, and material science are reviewed.
Journal ArticleDOI
Simulation of cardiac excitation patterns in a three-dimensional anatomical heart atlas
TL;DR: A three-dimensional atlas of the human heart, based on image data provided in the Visible Human Project, which consists of multiple kinds of cardiac tissues and offers unlimited possibilities for its visual exploration is presented.
Book ChapterDOI
The Games of Life
TL;DR: This work describes a set of mapping rules that must be applied to generate responses for various combinations of incoming signals in an automaton, a ‘black box’ which receives information and generates an output, choosing it from a fixed repertoire.
References
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Impulses and Physiological States in Theoretical Models of Nerve Membrane
TL;DR: Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle, which qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve.
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Concentration wave propagation in two-dimensional liquid-phase self-oscillating system.
TL;DR: This work deals with patterns in a thin layer of solution, in which cerium ions catalyse the oxidation of analogues of malonic acid by bromate by oscillations in the solution colour.
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A computer model of atrial fibrillation.
TL;DR: The model exhibited self-sustained turbulent activity having many similarities to atrial fibrillation, and suggests the formulation of a “fibrillation” number, similar in concept to the Reynolds number related to turbulence in fluid flow.
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Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction
TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.
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Spiral Waves of Chemical Activity
TL;DR: The Zhabotinsky-Zaikin reagent propagates waves of chemical activity that include spiral waves, resembling involutes of the circle, that appear, persist, and eventually exclude all concentric ring waves.