Computation of the drift velocity of spiral waves using response functions

I. V. Biktasheva, D. Barkley, V. N. Biktashev, A. J. Foulkes

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    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. © 2010 The American Physical Society.
    Original languageEnglish
    Article number066202
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Issue number6
    Publication statusPublished - 1 Jun 2010


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