@article{ParkRosenblumKurthsetal.1999, author = {Park, Eun Hyoung and Rosenblum, Michael and Kurths, J{\"u}rgen and Zaks, Michael A.}, title = {Alternating locking ratios in imperfect phase synchronization}, year = {1999}, 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{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} } @phdthesis{Zaks2001, author = {Zaks, Michael A.}, title = {Fractal Fourier spectra in dynamical systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000500}, school = {Universit{\"a}t Potsdam}, year = {2001}, abstract = {Eine klassische Art, die Dynamik nichtlinearer Systeme zu beschreiben, besteht in der Analyse ihrer Fourierspektren. F{\"u}r periodische und quasiperiodische Prozesse besteht das Fourierspektrum nur aus diskreten Deltafunktionen. Das Spektrum einer chaotischen Bewegung ist hingegen durch das Vorhandensein einer stetigen Komponente gekennzeichnet. In der Arbeit geht es um einen eigenartigen, weder regul{\"a}ren noch vollst{\"a}ndig chaotischen Zustand mit sogenanntem singul{\"a}rstetigen Leistungsspektrum. Unsere Analyse ergab verschiedene F{\"a}lle aus weit auseinanderliegenden Gebieten, in denen singul{\"a}r stetige (fraktale) Spektren auftreten. Die Beispiele betreffen sowohl physikalische Prozesse, die auf iterierte diskrete Abbildungen oder gar symbolische Sequenzen reduzierbar sind, wie auch Prozesse, deren Beschreibung auf den gew{\"o}hnlichen oder partiellen Differentialgleichungen basiert.}, subject = {Nichtlineares dynamisches System / Harmonische Analyse / Fraktal}, language = {en} } @article{FeudelTuckermanZaksetal.2017, author = {Feudel, Fred and Tuckerman, Laurette S. and Zaks, Michael and Hollerbach, Rainer}, title = {Hysteresis of dynamos in rotating spherical shell convection}, series = {Physical review fluids / American Physical Society}, volume = {2}, journal = {Physical review fluids / American Physical Society}, publisher = {American Physical Society}, address = {College Park}, issn = {2469-990X}, doi = {10.1103/PhysRevFluids.2.053902}, pages = {11}, year = {2017}, abstract = {Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Benard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or sub-critically and whether a direct link to the primary pure convective states exists is answered.}, language = {en} } @misc{TomovPenaRoqueetal.2016, author = {Tomov, Petar and Pena, Rodrigo F. O. and Roque, Antonio C. and Zaks, Michael A.}, title = {Mechanisms of self-sustained oscillatory states in hierarchical modular networks with mixtures of electrophysiological cell types}, series = {Frontiers in computational neuroscience}, journal = {Frontiers in computational neuroscience}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-407724}, pages = {17}, year = {2016}, abstract = {In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics "up" and "down" states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons. In particular, we observe that the crucial role both in interruption and in resumption of global activity is played by distributions of the membrane recovery variable within the network. We also demonstrate that the behavior of neurons is more influenced by their presynaptic environment in the network than by their formal types, assigned in accordance with their response to constant current.}, 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{TomovPenaRoqueetal.2016, author = {Tomov, Peter and Pena, Rodrigo F. O. and Roque, Antonio C. and Zaks, Michael A.}, title = {Mechanisms of Self-Sustained Oscillatory States in Hierarchical Modular Networks with Mixtures of Electrophysiological Cell Types}, series = {Frontiers in computational neuroscience / Frontiers Research Foundation}, volume = {10}, journal = {Frontiers in computational neuroscience / Frontiers Research Foundation}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, organization = {HESS Collaboration}, issn = {1662-5188}, doi = {10.3389/fncom.2016.00023}, pages = {476 -- +}, year = {2016}, abstract = {In a network with a mixture of different electrophysiological types of neurons linked by excitatory and inhibitory connections, temporal evolution leads through repeated epochs of intensive global activity separated by intervals with low activity level. This behavior mimics "up" and "down" states, experimentally observed in cortical tissues in absence of external stimuli. We interpret global dynamical features in terms of individual dynamics of the neurons. In particular, we observe that the crucial role both in interruption and in resumption of global activity is played by distributions of the membrane recovery variable within the network. We also demonstrate that the behavior of neurons is more influenced by their presynaptic environment in the network than by their formal types, assigned in accordance with their response to constant current.}, 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} }