## National Academy of Sciences of Ukraine## Scientific Centre for Medical and Biotechnical Research## Laboratory of Mathematical Modeling of Nonlinear Processes15 Bogdana Khmelnytskogo Str, room 401 ## Submitted for Publication## Spiral wave chimeras for coupled oscillators with inertia.EPJ
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.
## Chimera and solitary states in 3D oscillator networks with inertia.## https://arxiv.org/pdf/2002.08115.pdfVolodymyr Maistrenko, Oleksandr Sudakov, and Oleksiy Osiv
^{3} identical phase oscillators placed in a unit 3D cube with periodic boundary conditions. In the considered model with inertia, we have found novel types of patterns which do not exist in a pure system without inertia. In particular, a scroll wave torus-like chimera is obtained under random initial conditions. In contrast to a pure system without inertia, where all chimera states have incoherent inner parts, these states can have partially coherent or fully coherent inner parts in a system with inertia, as exemplified by a scroll wave torus-like 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.
## Recent Publications## Network-induced multistability through lossy coupling and exotic solitary states.Frank Hellmann, Paul Schultz, Patrycja Jaros, Roman Levchenko, Tomasz Kapitaniak, Jürgen Kurths and Yuri Maistrenko
Nature Communications 11:592 (2020); https://doi.org/10.1038/s41467-020-14417-7 ## The stability of synchronised networked systems is a multi-faceted challenge for manynatural and technologicalfields, from cardiac and neuronal tissue pacemakers to power grids.For these, the ongoing transition to distributed renewable energy sources leads to a pro-liferation of dynamical actors. The desynchronisation of a few or even one of those wouldlikely result in a substantial blackout. Thus the dynamical stability of the synchronous statehas become a leading topic in power grid research. Here we uncover that, when taking intoaccount physical losses in the network, the back-reaction of the network induces new exoticsolitary states in the individual actors and the stability characteristics of the synchronousstate are dramatically altered. These effects will have to be explicitly taken into account in thedesign of future power grids. We expect the results presented here to transfer to othersystems of coupled heterogeneous Newtonian oscillators. |