A. Sukiennicki

Generalizations of the concept of marginal synchronization of chaos

Abstract Generalizations of the concept of marginal synchronization between chaotic systems, i.e. synchronization with zero largest conditional Lyapunov exponent, are considered. Generalized marginal synchronization in drive–response systems is defined, for which the function between points of attractors of different systems is given up to a constant. Auxiliary system approach is shown to be able to detect this synchronization. Marginal synchronization in mutually coupled systems which can be viewed as drive–response systems with the response system influencing the drive system dynamics is also considered, and an example from solid-state physics is analyzed. Stability of these kinds of synchronization against changes of system parameters and noise is investigated. In drive–response systems generalized marginal synchronization is shown to be rather sensitive to the changes of parameters and may disappear either due to the loss of stability of the response system, or as a result of the blowout bifurcation. Nonlinear coupling of the drive system to the response system can stabilize marginal synchronization.

STOCHASTIC RESONANCE IN COUPLED THRESHOLD ELEMENTS WITH INPUT SIGNALS SHIFTED IN PHASE

Stochastic resonance in a system of two coupled threshold elements (neurons) forming a small artificial neural network is investigated. The elements have either antisymmetric or logistic (binary) response function and are driven by periodic signals and independent noises. Periodic signals at their inputs have equal amplitudes and frequencies but are shifted in phase. Depending on the response function and the phase shift, enhancement of stochastic resonance in individual elements, characterized by the output signal-to-noise ratio, and stochastic resonance with a spatiotemporal input signal, characterized by the correlation function between the input and output signals, are observed for proper coupling between elements.

Aperiodic stochastic resonance in chaotic maps

It is shown by means of numerical simulations that aperiodic stochastic resonance occurs in chaotic one-dimensional maps with various kinds of intermittency. The effect appears in the absence of external noise, as the system control parameter is varied. In the case of input signals slowly varying in time the analytic treatment, using the adiabatic approximation based on the expressions for the mean laminar phase duration, yields the input-output covariance function comparable with numerical results. (c) 1998 American Institute of Physics.

On-off intermittency in a high-dimensional model of randomly driven parallel pumping

Abstract A model of parallel pumping with many interacting parametric spin-wave pairs is investigated numerically. Two ways of obtaining on-off intermittency in the time series of absorption are discussed: random or chaotic modulation of the rf field amplitude or of the dc field, slow in comparison with the rf field frequency. If the possibility of thermal excitation of spin waves is neglected, only one spin-wave pair is excited above the intermittency threshold and exhibits bursts. In the opposite case, a phenomenon of widening of the phase space in the presence of thermal noise is observed: a packet of parametric spin waves is excited with frequencies close to half the pumping frequency. This modifies quantitatively, but not qualitatively the characteristics of on-off intermittency in the presence of thermal noise.

CHAOTIC DYNAMICS OF PERIODICALLY DRIVEN DOMAIN WALLS IN MAGNETIC GARNET FILMS

Abstract Nonlinear dynamics was investigated theoretically for the magnetic domain wall in a bubble garnet film for the case of the periodic drive field. Analysis of the phase trajectories, the Poincare sections and the spatio-temporal diagrams was performed. Pattern entropies, power spectral densities and correlation functions were analyzed. As a result, it was found that, depending on the period and amplitude of the drive field, a motion of the wall is periodic, quasi-periodic or chaotic. Very peculiar behaviour of the spatial correlation was found for the quasi-periodic and chaotic states.

Simulations of noise-free stochastic resonance in spin-wave chaos

Numerical simulations of noise-free stochastic resonance and aperiodic stochastic resonance in chaotic ferromagnetic resonance are presented. The model, based on three-magnon interactions between the externally excited uniform mode and pairs of spin waves, shows on-off intermittency. The rf magnetic field amplitude is slowly modulated by a small periodic or aperiodic signal, and the output signal, which reflects the occurrence of laminar phases and bursts in the time series of spin-wave amplitudes, is analyzed. On variation of the dc magnetic field the signal-to-noise ratio of the output signal and the correlation function between modulation and output signal pass a maximum, which indicates the occurrence of periodic and aperiodic stochastic resonance, respectively. The role of thermal magnon excitations in the occurrence of this maximum is clarified. The results are compared with experimental findings obtained in other types of intermittency. PACS numbers: 76.50.+g, 75.30.Ds, 05.45.+b, 05.40.+j