## 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## Solitary states in the mean-field limit.N. Kruk, Y. Maistrenko, and H. Koeppl We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise.By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models. ## Minimal Chimera States in Phase-Lag CoupledMechanical Oscillators.
EPJ We obtain experimental chimera states in the minimal net-work of three identical mechanical oscillators (metronomes), by intro-ducing phase-lagged all-to-all coupling. For this, we have developed areal-time model-in-the-loop coupling mechanism that allows for flexibleand online change of coupling topology, strength and phase-lag. Thechimera states manifest themselves as a mismatch of average frequencybetween two synchronous and one desynchronized oscillator. We findthis kind of striking chimeric behavior is robust in a wide parameterregion. At other parameters, however, chimera state can lose stabilityand the system behavior manifests itself as a heteroclinic switching be-tween three saddle-type chimeras. Our experimental observations arein a qualitative agreement with the model simulation. ## 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, the system behavior resembles
classical two-dimensional (2D) Kuramoto-Shima spiral chimeras with
bell-shape frequency characteristic of the incoherent cores. 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 (Poincar\'e
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.
## Recent Publications## Chimera and solitary states in 3D oscillator networks with inertia.30, 063113 (2020);
https://doi.org/10.1063/5.0005281 We report the diversity of scroll wave chimeras in the
three-dimensional (3D) Kuramoto model with inertia for N3 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 a pure 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. ## 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. |