• Open Access

Computation of the drift velocity of spiral waves using response functions

I. V. Biktasheva, D. Barkley, V. N. Biktashev, and A. J. Foulkes
Phys. Rev. E 81, 066202 – Published 1 June 2010

Abstract

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave’s center of rotation and fiducial phase may change over time, i.e., the spiral wave drifts. In linear approximation, the velocity of the drift is proportional to the convolution of the perturbation with the spiral’s response functions, which are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues λ=0,±iω. Here, we demonstrate that the response functions give quantitatively accurate prediction of the drift velocities due to a variety of perturbations: a time dependent, periodic perturbation (inducing resonant drift); a rotational symmetry-breaking perturbation (inducing electrophoretic drift); and a translational symmetry-breaking perturbation (inhomogeneity induced drift) including drift due to a gradient, stepwise, and localized inhomogeneity. We predict the drift velocities using the response functions in FitzHugh-Nagumo and Barkley models, and compare them with the velocities obtained in direct numerical simulations. In all cases good quantitative agreement is demonstrated.

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  • Received 21 January 2010

DOI:https://doi.org/10.1103/PhysRevE.81.066202

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Authors & Affiliations

I. V. Biktasheva

  • Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, United Kingdom

D. Barkley

  • Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

V. N. Biktashev

  • Department of Mathematical Sciences, University of Liverpool, Mathematical Sciences Building, Peach Street, Liverpool L69 7ZL, United Kingdom

A. J. Foulkes

  • Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, Liverpool L69 3BX, United Kingdom

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Issue

Vol. 81, Iss. 6 — June 2010

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