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Time-periodic lattice of spiral pairs in excitable media

A. Rabinovitch1,*, Y. Biton1, D. Braunstein2, M. Friedman3, and I. Aviram1

  • 1Physics Department, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel
  • 2Physics Department Shamoon College of Engineering, Beer-Sheva, Israel
  • 3Department of Information Systems Engineering, Ben-Gurion University, Beer Sheva 84105, Israel

  • *avinoam@bgu.ac.il
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Phys. Rev. E 85, 036217 – Published 30 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.036217

Abstract

The feasibility of a spiral-type solution, periodic both in time and in space, of a reaction-diffusion equation (specifically the FitzHugh-Nagumo system) in an excitable medium is numerically demonstrated. The solution consists of arrays of interacting spiral pairs, which repeatedly create by partial annihilation a system of residual portions (RPs). The latter behaves as a source to the next generation of the spiral-pair array. If basic (highest) translational symmetry is not conserved, pointwise perturbations, above a certain threshold, are shown to be able to destroy the pattern after a certain transient time by changing its symmetry. If the basic translational symmetry is preserved, such perturbations do not cause destruction unless occurring at the nearest vicinity of the RP site. Singular value decomposition methods are used to analyze the structure of the pattern, revealing the importance of the spiral pairs and the RPs.

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Phys. Rev. E 85, 036217– Published 30 March, 2012
  • Received 20 June 2011

©2012 American Physical Society

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