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Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

Hans Dierckx (UGent) , Alexander Panfilov (UGent) , Henri Verschelde (UGent) , VN Biktashev and IV Biktasheva
(2019) PHYSICAL REVIEW E. 99(2).
Author
Organization
Abstract
In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.
Keywords
3-DIMENSIONAL SCROLL WAVES, VORTEX DYNAMICS, MODEL, FILAMENTS, MEDIA, HYPERMEANDER, PROPAGATION, INSTABILITY, TRANSITION, VORTICES

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MLA
Dierckx, Hans, et al. “Response Function Framework for the Dynamics of Meandering or Large-Core Spiral Waves and Modulated Traveling Waves.” PHYSICAL REVIEW E, vol. 99, no. 2, 2019, doi:10.1103/physreve.99.022217.
APA
Dierckx, H., Panfilov, A., Verschelde, H., Biktashev, V., & Biktasheva, I. (2019). Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves. PHYSICAL REVIEW E, 99(2). https://doi.org/10.1103/physreve.99.022217
Chicago author-date
Dierckx, Hans, Alexander Panfilov, Henri Verschelde, VN Biktashev, and IV Biktasheva. 2019. “Response Function Framework for the Dynamics of Meandering or Large-Core Spiral Waves and Modulated Traveling Waves.” PHYSICAL REVIEW E 99 (2). https://doi.org/10.1103/physreve.99.022217.
Chicago author-date (all authors)
Dierckx, Hans, Alexander Panfilov, Henri Verschelde, VN Biktashev, and IV Biktasheva. 2019. “Response Function Framework for the Dynamics of Meandering or Large-Core Spiral Waves and Modulated Traveling Waves.” PHYSICAL REVIEW E 99 (2). doi:10.1103/physreve.99.022217.
Vancouver
1.
Dierckx H, Panfilov A, Verschelde H, Biktashev V, Biktasheva I. Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves. PHYSICAL REVIEW E. 2019;99(2).
IEEE
[1]
H. Dierckx, A. Panfilov, H. Verschelde, V. Biktashev, and I. Biktasheva, “Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves,” PHYSICAL REVIEW E, vol. 99, no. 2, 2019.
@article{8605272,
  abstract     = {{In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearized operator (i.e., response functions). For spiral waves, the finite radius of the spiral tip trajectory and spiral wave meander are taken into account. Different coordinate systems can be chosen, depending on whether one wants to predict the motion of the spiral-wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyze the drift of a meandering spiral wave in a constant external field in different regimes.}},
  articleno    = {{022217}},
  author       = {{Dierckx, Hans and Panfilov, Alexander and Verschelde, Henri and Biktashev, VN and Biktasheva, IV}},
  issn         = {{2470-0045}},
  journal      = {{PHYSICAL REVIEW E}},
  keywords     = {{3-DIMENSIONAL SCROLL WAVES,VORTEX DYNAMICS,MODEL,FILAMENTS,MEDIA,HYPERMEANDER,PROPAGATION,INSTABILITY,TRANSITION,VORTICES}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{20}},
  title        = {{Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves}},
  url          = {{http://doi.org/10.1103/physreve.99.022217}},
  volume       = {{99}},
  year         = {{2019}},
}
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