## 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 ## Recent Publications## Chimera complexity.Serhiy Brezetsky, Patrycja Jaros, Roman Levchenko, Tomasz Kapitaniak, and Yuri Maistrenko Phys. Rev. E 103, L050204 (2021) ;
https://journals.aps.org/pre/abstract/10.1103/PhysRevE.103.L050204 We show an amazing complexity of the chimeras in small networks of
coupled phase oscillators with inertia. The network behavior is
characterized by heteroclinic switching between multiple saddle chimera
states and riddling basins of attractions, causing an extreme
sensitivity to initial conditions and parameters. Additional uncertainty
is induced by the presumable coexistence of stable phase-locked states
or other stable chimeras as the switching trajectories can eventually
tend to them. The system dynamics becomes hardly predictable, while its
complexity represents a challenge in the network sciences. ## Solitary states in the mean-field limit.N. Kruk, Y. Maistrenko, and H. Koeppl Chaos 30, 111104 (2020);
https://doi.org/10.1063/5.0029585## Minimal Chimera States in Phase-Lag CoupledMechanical Oscillators.P. Ebrahimzadeh, M. Schiek, P. Jaros, T. Kapitaniak, S. van Waasen and Y. Maistrenko Eur. Phys. J. Special Topics
229, 2205 (2020). https://doi.org/10.1140/epjst/e2020-900270-4We 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.## 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. |