abstract

Noise-free stochastic resonance is investigated numerically in a system of two coupled chaotic Rössler oscillators. Periodic signal is applied either additively or multiplicatively to the coupling term. When the coupling constant is varied the oscillators lose synchronization via attractor bubbling or on–off intermittency. Properly chosen signals are analyzed which reflect the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. Maximum of the signal-to-noise ratio as a function of the coupling constant is observed. Dependence of the signal-to-noise ratio on the frequency of the periodic signal and parameter mismatch between the oscillators is investigated. Possible applications of stochastic resonance in the recovery of signals in secure communication systems based on chaotic synchronization are briefly discussed.

abstract

A model for noise-free stochastic resonance in chaotic nonlinear ferromagnetic resonance in coincidence regime is investigated numerically. In the model, interactions between the uniform mode and two pairs of parametric spin waves are taken into account. For certain values of the model parameters Pomeau–Maneville intermittency and on-off intermittency are observed. The case of slow periodic modulation of the rf field amplitude is considered and the signal analyzed reflects the sequence of laminar phases and bursts. Maximum of the signal-to-noise ratio is observed as the constant part of the rf field amplitude is varied in the neighbourhood of the intermittency threshold. The role of the thermal excitations of spin waves in the occurence of stochastic resonance is clarified. The results are in agreement with the recent experimental observations of stochastic resonance in spin-wave chaos.

abstract

Kinetic behaviour of dynamical information Shannon entropy is discussed for complex systems: physical systems with non-Markovian property and memory in correlation approximation, and biological and physiological systems with sequences of the Markovian and non-Markovian random noises. For the stochastic processes, a description of the information entropy in terms of normalized time correlation functions is given. The influence and important role of two mutually dependent channels of the entropy change, correlation (creation or generation of correlations) and anti-correlation (decay or annihilation of correlation) is discussed. The method developed here is also used in analysis of the density fluctuations in liquid cesium obtained from slow neutron scattering data, fractal kinetics of the long-range fluctuation in the short-time human memory and chaotic dynamics of R–R intervals of human ECG.

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The following paper is the continuation of our earlier considerations on cellular automata with Toom local rule (TCA) as the alternative to kinetic Ising systems. The arguments for TCA stationary states not being the equilibrium states are found in simulations.

abstract

A general method of analysis of non-stationary time series (time intervals of the human electrocardiogram) is presented: a short sliding window is used in conjunction with two different complexity measures. The first — a modified Shannon entropy called pattern entropy — quantifies the level of statistical order. The second is based on a symbolic dynamics in delay coordinate space and quantifies the level of sequential order by means of an estimator of algorithmic complexity. The sliding window procedure maps the original time series into a time series of the given complexity measure. The global state of the system is then characterized by the properties of the distribution of the resultant complexity measure. To characterize states on a local time scale the distribution of symbolic words is used. The method is applied to different data on heart rate variability, heart acceleration/deceleration and on the repolarization processes in the heart. We show that the nonlinear methods described may be applied to the analysis of the interaction of autonomic nervous system and the repolarization processes in the heart. This research was initiated to find new ways of prognosis the risk of sudden cardiac death. Below we show how the methods developed unveil new images of some physiological processes.

abstract

Starting with a discrete picture of the self-avoiding polygon embeddable in the square lattice, and utilizing both scaling arguments as well as a Steinhaus rule for evaluating the polygon’s area, we are able, by imposing a discrete time-dynamics and making use of the concept of quasi-static approximation, to arrive at some evolution rules for the surface fractal. The process is highly curvature-driven, which is very characteristic of many phenomena of biological interest, like crystallization, wetting, formation of biomembranes and interfaces. In a discrete regime, the number of subunits constituting the cluster is a nonlinear function of the number of the perimeter sites active for the growth. A change of the number of subunits in time is essentially determined by a change in the curvature in course of time, given explicitly by a difference operator. In a continuous limit, the process is assumed to proceed in time in a self-similar manner, and its description is generally offered in terms of a nonlinear dynamical system, even for the homogeneous clusters. For a sufficiently mature stage of the growing process, and when linearization of the dynamical system is realized, one may get some generalization of Mullins–Sekerka instability concept, where the function perturbing the circle is assumed to be everywhere continuous but not necessarily differentiable, like e.g. , the Weierstrass function. Moreover, a time-dependent prefactor appears in the simplified dynamical system.

abstract

Memory properties of the Hopfield type neural networks with four different types of dilution of synaptic connections (dilution inside blocks, dilution outside blocks and dilution of excitory/inhibitory synapses) as well as damaging of a part of neurons, are numerically investigated. Number of stored bits per neuron an stored bits per synapse for these networks were calculated and compared. Influence of the type of dilution on the memory properties of the network is discussed.