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THEORY OF DYNAMIC SYSTEMS:
- Research and development of methods for synchronization and control of dynamic and fluctuation-induced processes in nonlinear active systems;
- Research of occurrence mechanisms and characteristics of synchronization modes in ensembles of chaotic and stochastic dynamic systems;
- Theory of synchronization in networks of connected regular and chaotic systems.
Main results:
Leading expert:
Main technological and research equipment:
Main partners and customers:
Key projects (sources of financing):
Main publications:
Main results (comparable with the best world analogues):
- Foundations of the theory of phase synchronization in non-uniform ensembles of locally diffusely-connected regular and chaotic dynamic systems with continuous and discrete time have been developed;
- Existence of chaotic phase synchronization in ensembles of connected oscillators and in ensembles of connected rotators has been established. It has been shown that chaotic phase synchronization in many respects is similar to synchronization in the ensembles of periodic oscillators;
- It has been shown that transition to the synchronized phase behaviour of chaotic dynamic systems can occur through bifurcations or internal crises of chaotic attractors;
- A method of automatic phase synchronization in large ensembles of regular and chaotic dynamic systems connected by means of feedback loops has been proposed;
- The effect of cluster synchronization of elements in the ensembles of globally connected chaotic oscillators has been studied. Necessary conditions for the existence of conditional and unconditional clusters have been investigated. Besides, conditions of stability have been considered for isolated clusters.
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Leading expert:
- Grigory Vladimirovich Osipov, D.Sc. (Physics and Mathematics).
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Main technological and research equipment:
- Multiprocessor cluster of the Faculty of Computational Mathematics and Cybernetics with the following characteristics:
- Peak performance 2.7 TFLOPS;
- Total amount of core memory 256 Gb;
- 64 computing nodes;
- CPU: 2xIntel XEON 5150 Dual Core (4x2.66 Ghz cores);
- RAM: 4Gb DDR2;
- Analog-to-digital interface units of the type NI ELVIS with plug-in boards (National Instruments) – 6 pieces; DAQ-cards for data acquisition (National Instruments) – 7 pieces; specialized power supply unit UMP1503 (Quanser) – 1 piece.
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Main partners:
- Institute of Applied Physics of the Russian Academy of Sciences,
- Potsdam University (Germany),
- Leuven Catholic University (Belgium),
- Baptist University of Hong Kong (China).
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Key projects (sources of financing):
- INTAS Project (01-867).
- Projects of the Russian Foundation for Basic Research 03-02-17543- à , 05-02-19815-MF_ à , 06-02-16499- à , 06-02-16596- à , 08-02-92004-NNS_ à.
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Main publications:
- G.V. Osipov, J.Kurths, Ch. Zhou. Synchronization in oscillatory networks. Springer Series in Synergetics, 2007.
- V.N. Belykh, G.V.Osipov, V.S. Petrov, J.A.K. Suykens, J. Vandewalle. Cluster Synchronization in Oscillatory Networks. CHAOS, v.18, 2008.
- M.V. Ivanchenko, G.V.Osipov, V.D. Shalfeev, J.Kurths. A network mechanism for burst generation. Physical Review Letters, v.98, 2007.
- Kryukov A.K., Kanakov O.I., Osipov G.V. Waves of synchronization in the ensembles of weakly linear oscillators. Izvestiya VUZ «Applied Nonlinear Dynamics », V.17, 2009.
- A.K.Kryukov, G.V.Osipov, A.V.Polovinkin, and J.Kurths. Synchronous regimes in an ensemble of coupled Bonhoeffer-Van der Pol oscillators, Physical Review E, v.79,2009.
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