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Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation
I. V. Biktasheva, Y. E. Elkin, and V. N. Biktashev, “ Localized sensitivity of spiral waves in the complex Ginzburg-Landau equation,” Phys. Rev. E 57, 2656–2659 (1998).
V. N. Biktashev and A. V. Holden, “ Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities,” Chaos, Soliton Fractals 5, 575–622 (1995).
I. V. Biktasheva, Y. E. Elkin, and V. N. Biktashev, “ Resonant drift of spiral waves in the complex Ginzburg-Landau equation,” J. Biol. Phys. 25, 115–127 (1999).
I. V. Biktasheva and V. N. Biktashev, “ Response functions of spiral wave solutions of the complex Ginzburg-Landau equation,” J. Nonlinear Math. Phys. 8, 28–34 (2001).
I. V. Biktasheva, A. V. Holden, and V. N. Biktashev, “ Localization of response functions of spiral waves in the FitzHugh–Nagumo system,” Int. J. Bifurication Chaos 16, 1547–1555 (2006).
I. V. Biktasheva, H. Dierckx, and V. N. Biktashev, “ Drift of scroll waves in thin layers caused by thickness features: Asymptotic theory and numerical simulations,” Phys. Rev. Lett. 114, 068302 (2015).
V. N. Biktashev, I. V. Biktasheva, and N. A. Sarvazyan, “ Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone,” PLoS One 6, e24388 (2011).
O. A. Mornev, I. M. Tsyganov, O. V. Aslanidi, and M. A. Tsyganov, “ Beyond the Kuramoto-Zel'dovich theory: Steadily rotating concave spiral waves and their relation to the echo phenomenon,” J. Exp. Theor. Phys. Lett. 77, 270–275 (2003).
and D. Barkley
, “ Non-specular reflections in a macroscopic system with wave-particle duality: Spiral waves in bounded media
,” Chaos 23
); e-print arXiv:1304.0591
F. Fenton and A. Karma, “ Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation,” Chaos 8, 20–47 (1998).
A. Garzón, R. O. Grigoriev, and F. H. Fenton, “ Continuous-time control of alternans in long purkinje fibers,” Chaos 24, 033124 (2014).
J. M. Pastore, S. D. Girouard, K. R. Laurita, F. G. Akar, and D. S. Rosenbaum, “ Mechanism linking T-wave alternans to the genesis of cardiac fibrillation,” Circulation 99, 1385–1394 (1999).
J. B. Nolasco and R. W. Dahlen, “ A graphic method for the study of alternation in cardiac action potentials,” J. Appl. Physiol. 25, 191–196 (1968).
L. H. Frame and M. B. Simson, “ Oscillations of conduction, action potential duration, and refractoriness: A mechanism for spontaneous termination of reentrant tachycardias,” Circulation 78, 1277–1287 (1988).
C. D. Marcotte and R. O. Grigoriev, “ Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue,” Chaos 25, 063116 (2015).
G. Byrne, C. D. Marcotte, and R. O. Grigoriev, “ Exact coherent structures and chaotic dynamics in a model of cardiac tissue,” Chaos 25, 033108 (2015).
W. E. Arnoldi, “ The principle of minimized iterations in the solution of the matrix eigenvalue problem,” Q. Appl. Math. 9, 17–29 (1951).
Y. Saad and M. H. Schultz, “ GMres: A generalized minimal residual algorithm for solving nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 7, 856–869 (1986).
I. V. Biktasheva, D. Barkley, V. N. Biktashev, G. V. Bordyugov, and A. J. Foulkes, “ Computation of the response functions of spiral waves in active media,” Phys. Rev. E 79, 056702 (2009).
K. I. Agladze, V. A. Davydov, and A. S. Mikhailov, “ An observation of resonance of spiral waves in distributed excitable medium,” JETP Lett. 45, 767–770 (1987).
F. H. Fenton, S. Luther, E. M. Cherry, N. F. Otani, V. Krinksy, A. Pumir, E. Bodenschatz, and R. F. Gilmour, Jr., “ Termination of atrial fibrillation using pulsed low-energy far-field stimulation,” Circulation 120, 467–476 (2009).
A. Sandu, “ On the properties of runge-kutta discrete adjoints,” in Computational Science–ICCS 2006 ( Springer, 2006), pp. 550–557.
W. H. Enright, K. Jackson, S. P. Nørsett, and P. G. Thomsen, “ Interpolants for runge-kutta formulas,” ACM Trans. Math. Softw. (TOMS) 12, 193–218 (1986).
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This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.
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