Eur. Phys. J. Special Topics 229, 2327–2340 (2020)
https://doi.org/10.1140/epjst/e2020-900279-x

Regular Article

Spiral wave chimeras for coupled oscillators with inertia

¹ Scientific Center for Medical and Biotechnical Research, NAS of Ukraine, Volodymyrska Str. 54, 01030 Kyiv, Ukraine
² Taras Shevchenko National University of Kyiv, Volodymyrska Str. 60, 01030 Kyiv, Ukraine
³ Institute of Mathematics, NAS of Ukraine, Tereshchenkivska Str. 3, 01024 Kyiv, Ukraine

^a e-mail: maistren@nas.gov.ua

Received: 12 December 2019
Accepted: 8 June 2020
Published online: 28 September 2020

Abstract

We report the appearance and the metamorphoses of spiral wave chimera states in coupled phase oscillators with inertia. First, when the coupling strength is small enough, the system behavior resembles classical two-dimensional (2D) Kuramoto-Shima spiral chimeras with bell-shape frequency characteristic of the incoherent cores [Y. Kuramoto, S.I. Shima, Prog. Theor. Phys. Supp. 150, 115 (2003); S.I. Shima, Y. Kuramoto, Phys. Rev. E. 69, 036213 (2004)]. As the coupling increases, the cores acquire concentric regions of constant time-averaged frequencies, the chimera becomes quasiperiodic. Eventually, with a subsequent increase in the coupling strength, only one such region is left, i.e., the whole core becomes frequency-coherent. An essential modification of the system behavior occurs, when the parameter point enters the so-called solitary region. Then, isolated oscillators are normally present on the spiral core background of the chimera states. These solitary oscillators do not participate in the common spiraling around the cores; instead, they start to oscillate with different time-averaged frequencies (Poincaré winding numbers). The number and the disposition of solitary oscillators can be any, given by the initial conditions. At a further increase in the coupling, the spiraling disappears, and the system behavior passes to a sort of spatiotemporal chaos.