abstract

Noise-free aperiodic stochastic resonance is investigated numerically in a system of two coupled chaotic Rössler oscillators. The aperiodic input signal is obtained from a different chaotic system and applied either to one of the parameters of one oscillator or added to the coupling term. When the coupling constant is decreased the oscillators lose synchronization via attractor bubbling. The output signal is analyzed which reflects the sequence of synchronized (laminar) phases and non-synchronized bursts in the time evolution of the oscillators. The correlation function between the input and output signals shows maximum as a function of the coupling constant. The dependence of the correlation function on the mean frequency of oscillations of the input signal and on the parameter mismatch between the oscillators is very complex. The correlation increases non-monotonically with decreasing frequency, and the parameter mismatch can cause that the output and input signals are anticorrelated.

abstract

Stochastic resonance in a system of two coupled threshold elements (neurons) forming a small neural network is investigated numerically. Periodic signals at inputs of the elements are phase-shifted with respect to each other up to a half of the period, but their frequencies and amplitudes are identical. The signal-to-noise ratio at outputs of the elements has a maximum as a function of the input noise intensity for any phase shift. For proper coupling, dependent on the phase shift, this ratio is enhanced over that of a single uncoupled element. The enhancement is usually observed for positive (excitory) coupling if the phase shift is less than one fourth of the period, and for negative (inhibitory) coupling otherwise, but minor deviations from these rules are possible for high periodic signal frequency. Adiabatic theory of stochastic resonance in coupled threshold elements is also formulated which describes qualitatively the dependence of the signal-to-noise ratio on the coupling for various phase shifts.

abstract

The Penna model with simplifications aimed on elimination of randomness from the system dynamics is considered. In the deterministic system resulting, the relation arising from the Verhulst factor between families constituting the population is examined. An example of self-controlling chaotic system of two-families is presented.

abstract

We implement the Penna bit-string model of biological aging on a square lattice to study the evolution of the spatial distributions of the population when some rules for the coexistence for nearest lattice neighbors are introduced. By doing like this, we want to avoid the usage of the, so-called, Verhulst factor, which role has been disscused lately. The basic characteristics: population size, survival rates and mutation distribution, obtained in the lattice asexual Penna model occur different from the corresponding ones which are recorded in the standard Penna model.

abstract

The approximate method of solving the Smoluchowski equation for rotational diffusion of noninteracting rigid, dipolar and symmetric-top molecules under the action of the high intensity electric fields, within Kielich’s theory, is proposed. Employing the properties of the spherical harmonic functions and quantum-mechanical angular momentum operators, this paper extends the Kielich classical theory of nonlinear processes of the relaxation of the spherical top molecules for the case of the symmetric-top and for arbitrary shapes of the reorienting external fields.

abstract

Formulae are derived for the rise and decay relaxation functions of third-order electric polarization induced in liquids composed of dipolar, symmetric-top molecules by rectangular pulse with intermolecular interactions neglected. Smoluchowski equation for rotational diffusion of the symmetric-top molecules is applied.

abstract

The frequency-domain Havriliak–Negami and the time-domain Kohlrausch–Williams–Watts relaxation functions have found widespread acceptance in representing the relaxation data of dielectric systems. Since both functions yield an accurate description of real data in corresponding domains, a relationship between them is often suggested. In this paper we show that although a suitable choice of the parameters can lead in some ranges to a very small deviation between the plots of the functions, the empirical responses follow from clearly different mathematical reasons. We find a common probabilistic origin of both empirical relaxation functions. We obtain that the corresponding waiting-time distributions are infinitely divisible what may provide a clue to explain the universality observed in relaxation phenomena.

abstract

In the presented paper a new mathematical model of dispersion \(\beta \) in tissue dielectric response is introduced. It is proposed that interfacial phenomena and scaling properties of tissue account for power-law form of this region. The response \(\beta \) of tissue is considered with regard to probabilistic nature of its membrane components. The system is represented by an electric circuit of parallel \(R\)–\(C\) subcircuits with randomly distributed \(R\) and \(C\) values. It is shown that for the power law behaviour of tissue dielectric susceptibility \(\chi ( \omega )\) in the \(\beta \) response area the distribution of the variate \((R C)^{-1}\), representing the relaxation rate of a single subcircuit, should have heavy tails. The results indicate that the variations in local environment (local randomness) can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained fractal models.

abstract

The effects of neutral polymers on ion channel conductance have been used in the past to estimate channel radius. We have measured the effect of Polyethylene-glycol and dextrans on gramicidin-D, a peptide ion channel. The availability of high resolution structures of gramicidin-A allows us to make a direct comparison between the characteristic radius obtained by these experiments and the radius of the channel obtained from the NMR structure. The effects of PEG on gramicidin are significantly different from those observed on other, wider channels, and the experiment suggests that the operational size of the gramicidin channel exceeds that seen in the NMR and crystal structures. Our data using non-dehydrating polymers such as dextrans, provide estimates of gramicidin channel size smaller than those obtained with PEGs and closer to those predicted by the NMR and crystal structures.

abstract

Recent experimental data have demonstrated that DNA damage induced by densely ionizing radiation in mammalian cells is distributed along the DNA molecule in the form of clusters. The principal constituent of DNA damage are double-strand breaks (DSB) which are formed when the breaks occur in both DNA strands and are directly opposite or separated by only a few base pairs. DSBs are believed to be most important lesions produced in chromosomes by radiation; interaction between DSBs can lead to cell killing, mutation or carcinogenesis. The paper discusses a model of clustered DSB formation viewed in terms of compound Poisson process along with the predictive essay of the formalism in application to experimental data.

abstract

The influence of an external field on an ion current pattern in biological and synthetic systems was investigated. The patch clamp recordings of potassium current through a big conductance locust potassium channel (BK-channel) and a track-etched polyethylene terephthalate membrane were examined by the power spectrum, fractal analysis and relative dispersion analysis. A similar dependence of potassium current behaviour on the external voltage in both systems was found. The generalized dimension formalism is redefined to make it applicable to the analysis of time series.

abstract

Processes in coupled nonlinear systems are discussed under the influence of external signals and noise to improve the understanding of dynamical order and function in biological systems. A network of relaxation-type oscillators with nearest-neighbour coupling is numerically investigated under the influence of exponentially correlated noise. When all oscillators are exposed to an aperiodic subthreshold signal and to spatially incoherent noise, two regimes of behaviour are observed depending on the network’s coupling strength. In the case of weak coupling, noise at an intermediate level optimizes the correlation of the network oscillators with the aperiodic signal. In the case of stronger coupling the correlation with the external signal becomes lost, as intrinsic network dynamics take over. When the network is locally excited, noise-induced plane waves are built up, which move through the entire system. It is shown that the spatio-temporal pattern emerges independently of the way of the deterministic forcing. This effect may be understood as spatio-temporal stochastic resonance, since noise of an intermediate level optimizes the coherence of the wave-fronts.