TY - THES
A1 - Zaks, Michael A.
T1 - Fractal Fourier spectra in dynamical systems
N2 - Eine klassische Art, die Dynamik nichtlinearer Systeme zu beschreiben, besteht in der Analyse ihrer Fourierspektren. Für 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 regulären noch vollständig chaotischen Zustand mit sogenanntem singulärstetigen Leistungsspektrum. Unsere Analyse ergab verschiedene Fälle aus weit auseinanderliegenden Gebieten, in denen singulär 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 gewöhnlichen oder partiellen Differentialgleichungen basiert.
N2 - One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
KW - Nichtlineares dynamisches System / Harmonische Analyse / Fraktal
KW - Dynamische Systeme
KW - Leistungsspektrum
KW - Autokorrelation
KW - dynamical systems
KW - power spectrum
KW - autocorrelation
Y1 - 2001
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000500
ER -
TY - GEN
A1 - Tomov, Petar
A1 - Pena, Rodrigo F. O.
A1 - Roque, Antonio C.
A1 - Zaks, Michael A.
T1 - Mechanisms of self-sustained oscillatory states in hierarchical modular networks with mixtures of electrophysiological cell types
T2 - Frontiers in computational neuroscience
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 452
KW - self-sustained activity
KW - cortical oscillations
KW - irregular firing activity
KW - hierarchical modular networks
KW - cortical network models
KW - intrinsic neuronal diversity
KW - up-down states
KW - chaotic neural dynamics
Y1 - 2018
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-407724
ER -
TY - JOUR
A1 - Zaks, Michael A.
A1 - Pikovsky, Arkady S.
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 - http://dx.doi.org/10.1038/s41598-017-04918-9
SN - 2045-2322
VL - 7
PB - Macmillan Publishers Limited
CY - London
ER -
TY - GEN
A1 - Zaks, Michael A.
A1 - Pikovsky, Arkady S.
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 - Postprints 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 S.
A1 - Kurths, Jürgen
T1 - On the generalized dimensions for the fourier spectrum of the thue-morse sequence
Y1 - 1999
ER -
TY - INPR
A1 - Pikovsky, Arkady S.
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 - paper 015
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 - Park, Eun Hyoung
A1 - Kurths, Jürgen
T1 - On phase synchronization by periodic force in chaotic oscillators with saddle equilibria
Y1 - 2000
ER -
TY - JOUR
A1 - Pikovskij, Arkadij S.
A1 - Rosenblum, Michael G.
A1 - Zaks, Michael A.
A1 - Kurths, Jürgen
T1 - Phase synchronization of regular and chaotic oscillators
Y1 - 1999
ER -
TY - JOUR
A1 - Zaks, Michael A.
A1 - Rosenblum, Michael G.
A1 - Pikovskij, Arkadij S.
A1 - Osipov, Grigory V.
A1 - Kurths, Jürgen
T1 - Phase synchronization of chaotic oscillations in terms of periodic orbits
Y1 - 1997
SN - 1054-1500
ER -
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 - Park, Eun Hyoung
A1 - Rosenblum, Michael G.
A1 - Kurths, Jürgen
A1 - Zaks, Michael A.
T1 - Alternating locking ratios in imperfect phase synchronization
Y1 - 1999
ER -
TY - JOUR
A1 - Zaks, Michael A.
A1 - Pikovskij, Arkadij S.
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 S.
A1 - Kurths, Jürgen
T1 - On the correlation dimension of the spectral measure for the Thue-Morse sequence
Y1 - 1997
ER -
TY - JOUR
A1 - Osipov, Grigory V.
A1 - Rosenblum, Michael G.
A1 - Pikovskij, Arkadij S.
A1 - Zaks, Michael A.
A1 - Kurths, Jürgen
T1 - Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization
N2 - 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.
Y1 - 1997
ER -