Computation of the drift velocity of spiral waves using response functions
Biktasheva, I. V., Barkley, D., Biktashev, V. N. and Foulkes, A. J.. (2010) Computation of the drift velocity of spiral waves using response functions. Physical Review E, Vol.81 (No.6). Article no. 066202. ISSN 1539-3755
WRAP_Barkley_Computation_drift_velocity.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Available under License Creative Commons Attribution.
Official URL: http://dx.doi.org/10.1103/PhysRevE.81.066202
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 lambda=0, +/- i omega. 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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QC Physics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Waves -- Mathematical models|
|Journal or Publication Title:||Physical Review E|
|Publisher:||American Physical Society|
|Official Date:||1 June 2010|
|Number of Pages:||15|
|Page Range:||Article no. 066202|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Royal Society (Great Britain), Leverhulme Trust (LT), Engineering and Physical Sciences Research Council (EPSRC)|
|Grant number:||EP/D074789/1 (EPSRC), EP/D074746/1 (EPSRC)|
 T. Frisch, S. Rica, P. Coullet, and J. M. Gilli, Phys. Rev. Lett.
Actions (login required)