Chimera and solitary states in 3D oscillator networks with inertia

Abstract: We report the diversity of scroll wave chimeras in the three-dimensional (3D) Kuramoto model with inertia for N^{3} identical phase oscillators placed in a unit 3D cube with periodic boundary conditions. In the considered model with inertia, we have found patterns which do not exist in this system without inertia. In particular, a scroll ring chimera is obtained from random initial conditions. In contrast to this system without inertia, where all chimera states have incoherent inner parts, these states can have partially coherent or fully coherent inner parts as exemplified by a scroll ring chimera. Solitary states exist in the considered model as separate states or can coexist with scroll wave chimeras in the oscillatory space. We also propose a method of construction of 3D images using solitary states as solutions of the 3D Kuramoto model with inertia.