@article{ZaksPikovskij2019, author = {Zaks, Michael A. and Pikovskij, Arkadij}, title = {Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators}, series = {The European physical journal : B, Condensed matter and complex systems}, volume = {92}, journal = {The European physical journal : B, Condensed matter and complex systems}, number = {7}, publisher = {Springer}, address = {New York}, issn = {1434-6028}, doi = {10.1140/epjb/e2019-100152-2}, pages = {12}, year = {2019}, abstract = {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.}, 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{Symbolic dynamics behind the singular continuous power spectra of continuous flows}, year = {1998}, language = {en} } @unpublished{PikovskijZaksFeudeletal.1995, author = {Pikovskij, Arkadij and Zaks, Michael A. and Feudel, Ulrike and Kurths, J{\"u}rgen}, title = {Singular continuous spectra in dissipative dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13787}, year = {1995}, abstract = {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 Poincar{\´e} map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincar{\´e} 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.}, language = {en} } @article{PikovskijRosenblumZaksetal.1999, author = {Pikovskij, Arkadij and Rosenblum, Michael and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Phase synchronization of regular and chaotic oscillators}, year = {1999}, 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{ParkZaksKurths1999, author = {Park, Eun Hyoung and Zaks, Michael A. and Kurths, J{\"u}rgen}, title = {Phase synchronization in the forced lorenz system}, year = {1999}, language = {en} } @article{ZaksTomov2016, author = {Zaks, Michael A. and Tomov, Petar}, title = {Onset of time dependence in ensembles of excitable elements with global repulsive coupling}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {93}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.93.020201}, pages = {5}, year = {2016}, abstract = {We consider the effect of global repulsive coupling on an ensemble of identical excitable elements. An increase of the coupling strength destabilizes the synchronous equilibrium and replaces it with many attracting oscillatory states, created in the transcritical heteroclinic bifurcation. The period of oscillations is inversely proportional to the distance from the critical parameter value. If the elements interact with the global field via the first Fourier harmonics of their phases, the stable equilibrium is in one step replaced by the attracting continuum of periodic motions.}, language = {en} } @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{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} } @article{ZaksParkKurths2000, author = {Zaks, Michael A. and Park, Eun Hyoung and Kurths, J{\"u}rgen}, title = {On phase synchronization by periodic force in chaotic oscillators with saddle equilibria}, year = {2000}, language = {en} }