21953
1999
1999
eng
article
1
--
--
--
Alternating locking ratios in imperfect phase synchronization
allegro:1991-2014
10085144
Physical review letters. - 82 (1999), S. 4228 - 4231
Eun Hyoung Park
Michael Rosenblum
Jürgen Kurths
Michael A. Zaks
Institut für Physik und Astronomie
Institut für Physik
21339
1999
1999
eng
article
1
--
--
--
Phase synchronization of regular and chaotic oscillators
allegro:1991-2014
10086983
Handbook of chaos control / Hrsg.: H. G. Schuster. - Weinheim : Wiley-VCH, 1999. - S. 252 - 273
Arkadij Pikovskij
Michael Rosenblum
Michael A. Zaks
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
24923
1997
1997
eng
article
1
--
--
--
Phase synchronization of chaotic oscillations in terms of periodic orbits
1054-1500
allegro:1991-2014
10085211
Chaos : an interdisciplinary journal of nonlinear science. - ISSN 1054-1500. - 7 (1997), 4, S. 680 - 687
Michael A. Zaks
Michael Rosenblum
Arkadij Pikovskij
Grigory V. Osipov
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
24938
1997
1997
eng
article
1
--
--
--
Attractor-repeller collision and eyelet intermittency at the transition to phase synchronization
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.
allegro:1991-2014
10085209
Physical review letters. - 79 (1997), 1, S. 47 - 50
Grigory V. Osipov
Michael Rosenblum
Arkadij Pikovskij
Michael A. Zaks
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
44943
2016
2016
eng
7
94
article
American Physical Society
College Park
1
--
--
--
Anomalous transport in cellular flows: The role of initial conditions and aging
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.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.94.032128
27739722
2470-0045
2470-0053
wos2016:2019
032128
WOS:000383878700001
Poschke, P (reprint author), Humboldt Univ, Inst Phys, D-12489 Berlin, Germany., poeschke@physik.hu-berlin.de
German-Israeli Foundation for Scientific Research and Development (GIF) [I-1271-303.7/2014]
importub
2020-03-22T14:24:01+00:00
filename=package.tar
7ed0a3d48912264ca46001eafa8e7d15
Patrick Poeschke
Igor M. Sokolov
Alexander A. Nepomnyashchy
Michael A. Zaks
Institut für Physik und Astronomie
Referiert
Import
145
2001
eng
habilitation
1
2005-02-11
--
2002-06-20
Fractal Fourier spectra in dynamical systems
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.
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.
urn:nbn:de:kobv:517-0000500
47
UG 3900
Michael A. Zaks
deu
swd
Nichtlineares dynamisches System / Harmonische Analyse / Fraktal
deu
uncontrolled
Dynamische Systeme
deu
uncontrolled
Leistungsspektrum
deu
uncontrolled
Autokorrelation
eng
uncontrolled
dynamical systems
eng
uncontrolled
power spectrum
eng
uncontrolled
autocorrelation
Physik
open_access
Institut für Physik und Astronomie
Universität Potsdam
https://publishup.uni-potsdam.de/files/145/zaks.pdf
40772
2016
2018
eng
17
postprint
1
2018-06-28
2018-06-28
--
Mechanisms of self-sustained oscillatory states in hierarchical modular networks with mixtures of electrophysiological cell types
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.
Frontiers in computational neuroscience
urn:nbn:de:kobv:517-opus4-407724
online registration
Frontiers in computational neuroscience 10 (2016), Art. 23 ; DOI: 10.3389/fncom.2016.00023
CC-BY - Namensnennung 4.0 International
Petar Tomov
Rodrigo F. O. Pena
Antonio C. Roque
Michael A. Zaks
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
452
eng
uncontrolled
self-sustained activity
eng
uncontrolled
cortical oscillations
eng
uncontrolled
irregular firing activity
eng
uncontrolled
hierarchical modular networks
eng
uncontrolled
cortical network models
eng
uncontrolled
intrinsic neuronal diversity
eng
uncontrolled
up-down states
eng
uncontrolled
chaotic neural dynamics
Medizin und Gesundheit
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Institut für Physik und Astronomie
Referiert
Open Access
Frontiers
Universität Potsdam
https://publishup.uni-potsdam.de/files/40772/pmnr_452.online.pdf
45618
2016
2016
eng
5
93
article
American Physical Society
College Park
1
--
--
--
Onset of time dependence in ensembles of excitable elements with global repulsive coupling
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.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.93.020201
26986274
2470-0045
2470-0053
wos2016:2019
020201
WOS:000369735300001
Zaks, MA (reprint author), Univ Potsdam, Inst Phys & Astron, D-14465 Potsdam, Germany.; Tomov, P (reprint author), Humboldt Univ, Inst Phys, D-12489 Berlin, Germany., mzaks@uni-potsdam.de; tomov@mathematik.hu-berlin.de
DFG [IRTG 1740, PI 220/17-1]
importub
2020-03-22T20:02:01+00:00
filename=package.tar
26d3bece365373b2edb230a02028f6ed
Michael A. Zaks
Petar Tomov
Institut für Physik und Astronomie
Referiert
Import
45510
2016
2016
eng
476
+
17
10
article
Frontiers Research Foundation
Lausanne
HESS Collaboration
1
--
--
--
Mechanisms of Self-Sustained Oscillatory States in Hierarchical Modular Networks with Mixtures of Electrophysiological Cell Types
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.
Frontiers in computational neuroscience / Frontiers Research Foundation
10.3389/fncom.2016.00023
27047367
1662-5188
wos2016:2019
23
WOS:000372709900001
Roque, AC (reprint author), Univ Sao Paulo, Dept Phys, Sch Philosophy Sci & Letters Ribeirao Preto, Lab Sistemas Neurais, Sao Paulo, Brazil., antonior@ffciro.usp.br
IRTG [1740/TRP 2011/50150-0]; DFG/FAPESP; Research, Innovation and Dissemination Center for Neuromathematics FAPESP grant [2013/07699-0]; FAPESP scholarship [2013/25667-8, 2015/09916-3]; CNPq research grant [306251/2014-0]; DFG [PI 220/17-1]
importub
2020-03-22T19:05:02+00:00
filename=package.tar
b0ac94c2ed658dad86e5fd5cb79fb41c
Peter Tomov
Rodrigo F. O. Pena
Antonio C. Roque
Michael A. Zaks
eng
uncontrolled
self-sustained activity
eng
uncontrolled
cortical oscillations
eng
uncontrolled
irregular firing activity
eng
uncontrolled
hierarchical modular networks
eng
uncontrolled
cortical network models
eng
uncontrolled
intrinsic neuronal diversity
eng
uncontrolled
up-down states
eng
uncontrolled
chaotic neural dynamics
Institut für Physik und Astronomie
Referiert
Import
20303
2000
2000
eng
article
1
--
--
--
On phase synchronization by periodic force in chaotic oscillators with saddle equilibria
allegro:1991-2014
10097409
International Journal of Bifurcation and Chaos. - 10 (2000), 11, S. 2649 - 2667
Michael A. Zaks
Eun Hyoung Park
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
Nicht ermittelbar
21118
1999
1999
eng
article
1
--
--
--
Phase synchronization in the forced lorenz system
allegro:1991-2014
10085121
Physical review / E. - 60 (1999), S. 6627 - 6638
Eun Hyoung Park
Michael A. Zaks
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
48926
2019
2019
eng
12
7
92
article
Springer
New York
1
--
2019-07-22
--
Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators
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.
The European physical journal : B, Condensed matter and complex systems
10.1140/epjb/e2019-100152-2
1434-6028
1434-6036
wos:2019
160
WOS:000476541600002
Zaks, MA (reprint author), Humboldt Univ, Inst Phys, Berlin, Germany.; Zaks, MA (reprint author), Lobachevsky Univ Nizhni Novgorod, Dept Control Theory, Nizhnii Novgorod, Russia., zaks@physik.hu-berlin.de
DFGGerman Research Foundation (DFG) [PI 220/17-1]; Russian Science FoundationRussian Science Foundation (RSF) [17-12-01534]
2021-01-15T09:38:06+00:00
sword
importub
filename=package.tar
7b832e95a75ba60026fa247f022d5d57
Zaks, Michael A
false
true
Michael A. Zaks
Arkadij Pikovskij
eng
uncontrolled
Statistical and Nonlinear Physics
Physik
Institut für Physik und Astronomie
Referiert
Import
Green Open-Access
1254
1995
eng
preprint
1
2007-06-06
--
--
Singular continuous spectra in dissipative dynamics
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.
urn:nbn:de:kobv:517-opus-13787
1378
-
Arkadij Pikovskij
Michael A. Zaks
Ulrike Feudel
Jürgen Kurths
NLD Preprints
15
Physik
open_access
Institut für Physik und Astronomie
Interdisziplinäres Zentrum für Dynamik komplexer Systeme
Universität Potsdam
https://publishup.uni-potsdam.de/files/1254/preprint_pikovsky_etal.pdf
21090
1999
1999
eng
article
1
--
--
--
On the generalized dimensions for the fourier spectrum of the thue-morse sequence
allegro:1991-2014
10085145
Journal of physics / A. - 32 (1999), S. 1523 - 1530
Michael A. Zaks
Arkadij Pikovskij
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
22658
1998
1998
eng
article
1
--
--
--
Symbolic dynamics behind the singular continuous power spectra of continuous flows
allegro:1991-2014
10085185
Physica / D. - 117 (1998), 3, S. 77 - 94
Michael A. Zaks
Arkadij Pikovskij
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
24166
1997
1997
eng
article
1
--
--
--
On the correlation dimension of the spectral measure for the Thue-Morse sequence
allegro:1991-2014
10085230
Journal of statistical physics. - 88 (1997), 5/6, S. 1387 - 1392
Michael A. Zaks
Arkadij Pikovskij
Jürgen Kurths
Institut für Physik und Astronomie
Institut für Physik
40218
2017
2017
eng
10
postprint
1
--
2017-10-20
--
Chimeras and complex cluster states in arrays of spin-torque oscillators
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.
urn:nbn:de:kobv:517-opus4-402180
online registration
Scientific reports 7 (2017). - DOI: 10.1038/s41598-017-04918-9
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40216">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC-BY - Namensnennung 4.0 International
Michael A. Zaks
Arkadij Pikovskij
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
384
Informatik, Informationswissenschaft, allgemeine Werke
Chemie und zugeordnete Wissenschaften
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/40218/pmnr384_online.pdf
40216
2017
2017
eng
7
article
Macmillan Publishers Limited
London
1
--
2017-07-05
--
Chimeras and complex cluster states in arrays of spin-torque oscillators
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.
Scientific reports
10.1038/s41598-017-04918-9
28680160
2045-2322
Universität Potsdam, Publikationsfonds
PA 2017_32
1552.95
online registration
4648
WOS:000404846000021
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402180">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 384</a>
CC-BY - Namensnennung 4.0 International
Michael A. Zaks
Arkadij Pikovskij
Informatik, Informationswissenschaft, allgemeine Werke
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam