@article{ZaksPikovskijKurths1999, author = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {On the generalized dimensions for the fourier spectrum of the thue-morse sequence}, year = {1999}, language = {en} } @article{ZaksPikovskijKurths1998, author = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Symbolic dynamics behind the singular continuous power spectra of continuous flows}, year = {1998}, language = {en} } @article{ZaksPikovskijKurths1997, author = {Zaks, Michael A. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {On the correlation dimension of the spectral measure for the Thue-Morse sequence}, year = {1997}, language = {en} } @misc{ZaksPikovskij2017, author = {Zaks, Michael A. and Pikovskij, Arkadij}, title = {Chimeras and complex cluster states in arrays of spin-torque oscillators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402180}, pages = {10}, year = {2017}, abstract = {We consider synchronization properties of arrays of spin-torque nano-oscillators coupled via an RC load. We show that while the fully synchronized state of identical oscillators may be locally stable in some parameter range, this synchrony is not globally attracting. Instead, regimes of different levels of compositional complexity are observed. These include chimera states (a part of the array forms a cluster while other units are desynchronized), clustered chimeras (several clusters plus desynchronized oscillators), cluster state (all oscillators form several clusters), and partial synchronization (no clusters but a nonvanishing mean field). Dynamically, these states are also complex, demonstrating irregular and close to quasiperiodic modulation. Remarkably, when heterogeneity of spin-torque oscillators is taken into account, dynamical complexity even increases: close to the onset of a macroscopic mean field, the dynamics of this field is rather irregular.}, language = {en} } @article{ZaksPikovskij2017, author = {Zaks, Michael A. and Pikovskij, Arkadij}, title = {Chimeras and complex cluster states in arrays of spin-torque oscillators}, series = {Scientific reports}, volume = {7}, journal = {Scientific reports}, publisher = {Macmillan Publishers Limited}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-017-04918-9}, year = {2017}, abstract = {We consider synchronization properties of arrays of spin-torque nano-oscillators coupled via an RC load. We show that while the fully synchronized state of identical oscillators may be locally stable in some parameter range, this synchrony is not globally attracting. Instead, regimes of different levels of compositional complexity are observed. These include chimera states (a part of the array forms a cluster while other units are desynchronized), clustered chimeras (several clusters plus desynchronized oscillators), cluster state (all oscillators form several clusters), and partial synchronization (no clusters but a nonvanishing mean field). Dynamically, these states are also complex, demonstrating irregular and close to quasiperiodic modulation. Remarkably, when heterogeneity of spin-torque oscillators is taken into account, dynamical complexity even increases: close to the onset of a macroscopic mean field, the dynamics of this field is rather irregular.}, language = {en} } @article{PoeschkeSokolovNepomnyashchyetal.2016, author = {Poeschke, Patrick and Sokolov, Igor M. and Nepomnyashchy, Alexander A. and Zaks, Michael A.}, title = {Anomalous transport in cellular flows: The role of initial conditions and aging}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {94}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.94.032128}, pages = {7}, year = {2016}, abstract = {We consider the diffusion-advection problem in two simple cellular flow models ( often invoked as examples of subdiffusive tracer motion) and concentrate on the intermediate time range, in which the tracer motion indeed may show subdiffusion. We perform extensive numerical simulations of the systems under different initial conditions and show that the pure intermediate-time subdiffusion regime is only evident when the particles start at the border between different cells, i.e., at the separatrix, and is less pronounced or absent for other initial conditions. The motion moreover shows quite peculiar aging properties, which are also mirrored in the behavior of the time-averaged mean squared displacement for single trajectories. This kind of behavior is due to the complex motion of tracers trapped inside the cell and is absent in classical models based on continuous-time random walks with no dynamics in the trapped state.}, language = {en} } @article{ZaksRosenblumPikovskijetal.1997, author = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillations in terms of periodic orbits}, issn = {1054-1500}, year = {1997}, language = {en} } @article{OsipovRosenblumPikovskijetal.1997, author = {Osipov, Grigory V. and Rosenblum, Michael and Pikovskij, Arkadij and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization}, year = {1997}, abstract = {The chaotically driven circle map is considered as the simplest model ofphase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.}, language = {en} }