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Author: Maistrenko, Yuri ×

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    Network-induced multistability through lossy coupling and exotic solitary states
    ([London] : Nature Publishing Group UK, 2020) Hellmann, Frank; Schultz, Paul; Jaros, Patrycja; Levchenko, Roman; Kapitaniak, Tomasz; Kurths, Jürgen; Maistrenko, Yuri
    The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. For these, the ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronisation of a few or even one of those would likely result in a substantial blackout. Thus the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we uncover that, when taking into account physical losses in the network, the back-reaction of the network induces new exotic solitary states in the individual actors and the stability characteristics of the synchronous state are dramatically altered. These effects will have to be explicitly taken into account in the design of future power grids. We expect the results presented here to transfer to other systems of coupled heterogeneous Newtonian oscillators.
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    Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally coupled phase oscillators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Omel'chenko, Oleh; Wolfrum, Matthias; Yanchuk, Serhiy; Maistrenko, Yuri; Sudakov, Oleksandr
    Recently it has been shown that large arrays of identical oscillators with non-local coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motion, often called chimera states. We present here a detailed numerical study of the appearance of such solutions in twodimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, the stationarity means that for increasing system size the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation
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    From synchronization to Lyapunov exponents and back
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Politi, Antonio; Ginelli, Francesco; Yanchuk, Serhiy; Maistrenko, Yuri
    The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble- rather than time-averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase-synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rössler oscillator.