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Spiral wave dynamics in excitable media with spherical geometries
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10.1063/1.2346237
/content/aip/journal/chaos/16/3/10.1063/1.2346237
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/3/10.1063/1.2346237
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Symmetric spiral solution on a sphere. Top (a), bottom (b), and side (c) views of the sphere. Also shown in (d) is the time evolution of the spiral tip locations when .

Image of FIG. 2.
FIG. 2.

(Color online) Example of a random initial condition on a thin spherical shell whose outer radius is . The two panels show two different views of the sphere with 30 initial segments. Red (or black) regions represent excited domains, blue (or light gray) refractory domains, and green (or dark gray) regions are cells at rest.

Image of FIG. 3.
FIG. 3.

(Color) Snapshots of spiral waves on spherical shells with for various values of (panels on left) and plots of the locations of the singularities every 100 time steps during a time interval of length 5000 (panels on right). Red circles represent locations of the singularities with , while blue crosses are used for . (a) with a right view of the sphere (left panel) and singularity dynamics during . (b) with a right view of the sphere and singularity dynamics for . (c) with a top view of the sphere and locations of singularities for . (d) with a top view of the sphere and location of the singularities for .

Image of FIG. 4.
FIG. 4.

Plots of the average number of singularities as a function of time for spherical shells with for various values of . See text for details.

Image of FIG. 5.
FIG. 5.

(Color) (a) Left and right views of a spherical shell with for , together with a plot of the location of the singularities for every time step in the range in (b).

Image of FIG. 6.
FIG. 6.

A plot of for as a function of time for (solid circles), (unfilled circles), and (solid squares).

Image of FIG. 7.
FIG. 7.

(Color online) Front and back views of a sphere for with showing a pair of three-armed spirals at .

Image of FIG. 8.
FIG. 8.

Spiral configurations on 2D rectangular domains with no-flux boundary conditions for (a) at time 7500, (b) at time 7500, (c) at time 10 000, and (d) at time 7500. The formation of several clusters of occurs in all cases except for . For , the pair of four-armed spirals appears early in the simulation, and persists for the duration of the simulation.

Image of FIG. 9.
FIG. 9.

A scroll wave filament in a solid sphere of excitable medium with radius in the form of an arc of a circle with radius . This geometry was used to obtain the solution to Eq. (8) given in Eq. (9) .

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/content/aip/journal/chaos/16/3/10.1063/1.2346237
2006-09-27
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spiral wave dynamics in excitable media with spherical geometries
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/3/10.1063/1.2346237
10.1063/1.2346237
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