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Spiral Wave Chimera

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Book cover Synchronization and Waves in Active Media

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Abstract

A spiral wave chimera is the union of spiral waves [1] and chimeras states [2] - two paradigms in spatial pattern formation and temporal synchronization [3]. Spiral waves have been researched extensively in simulations as well as experiments during the last 70 years [4] in excitable media due to their spontaneous formation in a plethora of natural systems (see the introduction of Chap. 2 for examples). A spiral wave nucleates from the open end of an excitation wave. The open end curls in and becomes the center of the spiral wave from which waves are periodically emitted. The chimera state was numerically found by Yoshiki Kuramoto about 15 years ago (In 2001 Kuramoto presented his findings on nonlocally coupled systems, that already encompassed one- and two-dimensional problems, at a meeting named “Nonlinear Dynamics and Chaos: Where do we go from here?” in Bristol, United Kingdom. Subsequently his work, on what later became known as chimera state [5], was published as a chapter [6] in the accompanying conference monograph [7].), when he extended his model for synchronization in networks from globally to nonlocally coupled oscillators. While dissipative oscillators with identical frequencies in a globally coupled system trivially synchronize, this is not the case for nonlocal coupling. Two groups emerge: One coherent group, which is frequency-synchronized and another incoherent one, which is desynchronized.

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Notes

  1. 1.

    In 2001 Kuramoto presented his findings on nonlocally coupled systems, that already encompassed one- and two-dimensional problems, at a meeting named “Nonlinear Dynamics and Chaos: Where do we go from here?” in Bristol, United Kingdom. Subsequently his work, on what later became known as chimera state [5], was published as a chapter [6] in the accompanying conference monograph [7].

  2. 2.

    Since the pattern is discontinuous, the phase singularity is not localized at a single point, as for regular spiral waves with a continuous concentration field. Instead the singularity is spread out over the entire core region.

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Totz, J.F. (2019). Spiral Wave Chimera. In: Synchronization and Waves in Active Media. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-11057-4_4

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