TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Nikolaev, S
A1  - Kurths, Jürgen
T1  - Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions
N2  - We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place
Y1  - 2006
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.73.056202
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Kopeikin, A. S.
A1  - Kurths, Jürgen
T1  - Studying hyperbolicity in chaotic systems
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Zakharova, Anna
A1  - Vadivasova, Tatjana
A1  - Anishchenko, Vadim S.
A1  - Koseska, Aneta
A1  - Kurths, Jürgen
T1  - Stochastic bifurcations and coherencelike resonance in a self-sustained bistable noisy oscillator
N2  - We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.81.011106
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Vadivasova, T. E.
A1  - Kopeikin, A. S.
A1  - Strelkova, G. I.
A1  - Kurths, Jürgen
T1  - Spectral and correlation analysis of spiral chaos
N2  - We study numerically the behavior of the autocorrelation function (ACF) and the power spectrum of spiral attractors without and in the presence of noise. It is shown that the ACF decays exponentially and has two different time scales. The rate of the ACF decrease is defined by the amplitude fluctuations on small time intervals, i.e., when tau < tau(cor), and by the effective diffusion coefficient of the instantantaneous phase on large time intervals. it is also demonstrated that the ACF in the Poincare map also decreases according to the exponential law exp(-lambda(+)k), where lambda(+) is the positive Lyapunov exponent. The obtained results are compared with the theory of fluctuations for the Van der Pol oscillator
Y1  - 2003
SN  - 0219-4775
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Kopeikin, A. S.
A1  - Vadivasova, T. E.
T1  - Influence of noise on statistical properties of nonhyperbolic attractors
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Vadivasova, T. E.
A1  - Kopeikin, A. S.
A1  - Kurths, Jürgen
A1  - Strelkova, G. I.
T1  - Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors
Y1  - 2001
ER  - 
TY  - JOUR
A1  - Anishchenko, Vadim S.
A1  - Vadivasova, T. E.
A1  - Kurths, Jürgen
A1  - Okrokvertskhov, G. A.
A1  - Strelkova, G. I.
T1  - Autocorrelation function and spectral linewidth of spiral chaos in a physical experiment
N2  - We present results of physical experiments where we measure the autocorrelation function (ACF) and the spectral linewidth of the basic frequency of a spiral chaotic attractor in a generator with inertial nonlinearity both without and in the presence of external noise. It is shown that the ACF of spiral attractors decays according to an exponential law with a decrement which is defined by the phase diffusion coefficient. It is also established that the evolution of the instantaneous phase can be approximated by a Wiener random process
Y1  - 2004
SN  - 1063-651X
ER  -