Spiral wave chimeras for coupled oscillators with inertia

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, system's behavior resembles classical 2D Kuramoto chimeras with bell-shape frequency characteristic of the incoherent core. As the coupling increases, the core obtains concentric regions with different constant frequencies, which means that a chimera becomes quasiperiodic . Eventually, with a subsequent increase in the coupling strength, only one such region is left: all oscillators in the core become frequency-coherent. An essential modification of system's behavior occurs, when the parameter point enters the so-called "solitary" parameter region, where isolated oscillators can arise inside the spiral background. These solitary oscillators do not participate in the common spiraling around the cores. Instead, they start to rotate with an average frequency different from both spiral and core ones. The disposition of solitary oscillators can be any, as it is given by the initial conditions. At a further increase in the coupling, the spiraling disappears, and the system passes to a spatial or spatiotemporal chaos