On the Movement of Excitation Wave Breaks

The Large Core Limit of Spiral Waves in Excitable Media: A Numerical Approach

“…We can clearly identify a linear scaling regime ω ∼ (ǫ − ǫ c ) 1 and r c ∼ (ǫ − ǫ c ) −1 (5.4) at the bifurcation. This scaling behaviour was predicted in [12] using kinematic theory, and in [1] using equivariant bifurcation theory. The change from a rigidly rotating spiral to a travelling wave finger was described as a so called drift bifurcation 1 which occurs in the group dynamics rather than in the shape dynamics.…”

“…Whereas the bifurcation to meandering spirals is well-understood numerically and theoretically [3,51,14,17,37,38], the latter one is not. Theoretically, several attempts have been made to study this large core limit, using kinematic theory [53,43,12,32,22,23,52,13], dynamical systems theory [1] and non-perturbative asymptotics [20]. Computational results, on the other hand, are rare.…”

Riding a spiral wave: Numerical simulation of spiral waves in a comoving frame of reference

“…We have also investigated the vicinity of the "∂R" manifold in the parametric space, which has provided a strong evidence towards one of the two theoretical possible asymptotics, namely Elkin et al [47] asymptotics as opposed to Hakim-Karma [45] asymptotics. It should be noted here that while Hakim-Karma asymptotic theory was based on assumptions which have been well established, the Elkin et al asymptotic theory was using assumptions, validity of which could not be asserted at that moment.…”

“…where p is a parameter of the model such that p = p * corresponds to the ∂R boundary. Elkin et al [47] obtained an alternative asymptotic based on assumptions which were not restricted to kinetics of any particular kind, but which were not directly validated. Their prediction was…”

Untitled

“…There are limiting cases where some results can be achieved analytically. The 'kinematic approach' [12,13] applies to an important class of excitation waves, which include the waves in heart tissue. If the excitation waves are rare and locally nearly planar, then the description of a wave is reduced to the description of a jobp331.tex; 19/07/1999; 20:48; p.1 WTB: JOBP331; pips: 207640; GSB web2c: 708035 (jobpkap:mathfam) v. 1.15 curve, the crest line of the wave, and motion of this curve is determined by its local geometry.…”