TY - JOUR A1 - Park, Eun Hyoung A1 - Zaks, Michael A. A1 - Kurths, Jürgen T1 - Phase synchronization in the forced lorenz system Y1 - 1999 ER - TY - JOUR A1 - Zaks, Michael A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators JF - Scientific reports N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-04918-9 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij T1 - Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators JF - The European physical journal : B, Condensed matter and complex systems N2 - We consider collective dynamics in the ensemble of serially connected spin-torque oscillators governed by the Landau-Lifshitz-Gilbert-Slonczewski magnetization equation. Proximity to homoclinicity hampers synchronization of spin-torque oscillators: when the synchronous ensemble experiences the homoclinic bifurcation, the growth rate per oscillation of small deviations from the ensemble mean diverges. Depending on the configuration of the contour, sufficiently strong common noise, exemplified by stochastic oscillations of the current through the circuit, may suppress precession of the magnetic field for all oscillators. We derive the explicit expression for the threshold amplitude of noise, enabling this suppression. KW - Statistical and Nonlinear Physics Y1 - 2019 U6 - https://doi.org/10.1140/epjb/e2019-100152-2 SN - 1434-6028 SN - 1434-6036 VL - 92 IS - 7 PB - Springer CY - New York ER - TY - INPR A1 - Pikovskij, Arkadij A1 - Zaks, Michael A. A1 - Feudel, Ulrike A1 - Kurths, Jürgen T1 - Singular continuous spectra in dissipative dynamics N2 - We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique. T3 - NLD Preprints - 15 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13787 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - On the generalized dimensions for the fourier spectrum of the thue-morse sequence Y1 - 1999 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - Symbolic dynamics behind the singular continuous power spectra of continuous flows Y1 - 1998 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij A1 - Kurths, Jürgen T1 - On the correlation dimension of the spectral measure for the Thue-Morse sequence Y1 - 1997 ER - TY - GEN A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 384 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-402180 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators JF - Scientific reports N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-04918-9 SN - 2045-2322 VL - 7 PB - Macmillan Publishers Limited CY - London ER - TY - JOUR A1 - Poeschke, Patrick A1 - Sokolov, Igor M. A1 - Nepomnyashchy, Alexander A. A1 - Zaks, Michael A. T1 - Anomalous transport in cellular flows: The role of initial conditions and aging JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.94.032128 SN - 2470-0045 SN - 2470-0053 VL - 94 PB - American Physical Society CY - College Park ER -