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 -