# Spiral wave dynamics in excitable media with spherical geometries.

@article{Rohlf2006SpiralWD, title={Spiral wave dynamics in excitable media with spherical geometries.}, author={Katrin Rohlf and Leon Glass and Raymond Kapral}, journal={Chaos}, year={2006}, volume={16 3}, pages={ 037115 } }

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two…

## 12 Citations

Evolution of Spiral Waves in Excitable Systems

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This study extends the results on pattern formation in [27] to include investigations on the spiral wave phenomenology and shows that spiral waves emerge because of the interplay between two specific model parameters: one regulating the oscillatory dynamics in the kinetics and the other one related to the domain size.

Ginzburg-Landau patterns in circular and spherical geometries: vortices, attractors and spirals.

- Mathematics
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We prove that each equilibrium of the Ginzburg-Landau equation restricted to the invariant subspace of $m$-armed vortex solutions is hyperbolic, that is, its associated linearized operator possesses…

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- Computer Science, MedicineHFSP journal
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It is shown how the choice of biperiodic boundary conditions sustains fibrillation for a longer duration than no‐flux boundary conditions for a given area, and so is commonly invoked, leading to a boundary condition artifact that may complicate the analysis of defibrillation efficacy.

Turing pattern formation on the sphere for a morphochemical reaction-diffusion model for electrodeposition

- Mathematics, Computer ScienceCommun. Nonlinear Sci. Numer. Simul.
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The reaction-diffusion system for metal electrodeposition introduced in Bozzini et al., J. Solid State Electr.

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The results show that the multiscale ventricle model is capable of simulating mechanical contraction, pressure generation and load interactions as well as demonstrating the individual contribution of each ion current.

Splitting-based schemes for numerical solution of nonlinear diffusion equations on a sphere

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2013

An advanced study of the recently developed method for the numerical solution of nonlinear diffusion equations on a sphere, which shows that the competition of the three basic mechanisms-the nonlinear interaction, forcing and dissipation-can generate wave solutions that are subjected to the alternating influence of the processes of self-organisation and self-destruction.

Spiral Waves in a Lattice Array of Josephson Junction Chaotic Oscillators with Flux Effects

- PhysicsMathematical Problems in Engineering
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Josephson junction devices play a significant role in various physical nonlinear systems because of their complex characteristics. Chaotic phenomenon in various types of Josephson junction devices…

A guide to modelling cardiac electrical activity in anatomically detailed ventricles.

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