Intrinsic electronic noise strength significantly alters a period doubling cascade to chaos.

For universality in the approach, it is customary to appropriately rescale problems to a single or a set of dimensionless equations with dimensionless quantities involved or to rescale the experimental setup to a suitable size for the laboratory conditions. Theoretical results and/or experimental findings are supposed to be valid for both the original and the rescaled problems. Here, however, we show in an analog computer model nonlinear system how the experimental results depend on the scale factor.

Active particles with broken symmetry.

We discuss and analyze the driving a polar active particle with a head-tail asymmetry based on the dynamics of an internal motor variable driven by an energy depot and a broken symmetry of friction with respect to the internal degree of freedom. We show that such a driving may be advantageous for driving large masses with small energy uptake from the environment and exhibits interesting properties such as resonance-driven optimal propulsion.

Harmonic oscillator under Lévy noise: unexpected properties in the phase space.

A harmonic oscillator under the influence of noise is a basic model of various physical phenomena. Under Gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate Gaussian distribution with elliptic level lines. The distribution of phase is homogeneous.

Anharmonicity and its significance to non-Ohmic electric conduction.

We provide here a thorough analysis of the interplay between anharmonic lattice dynamics (with exponential repulsion between units) and electric conduction in a driven-dissipative electrically charged one-dimensional system. First, we delineate the ranges of parameter values where, respectively, subsonic and supersonic wave solitons are possible along the lattice. Then, we study the consequences of the soliton-mediated coupling of light negative to heavy positive charges (lattice units).

New species in evolving networks--stochastic theory of sensitive networks and applications on the metaphorical level.

In this paper we develop a theory to describe stochastic influences on the fate of new species with non-linear growth rates in evolutionary processes. We develop a theoretical framework based on notions of species, network, innovation, competition, survival and fitness. We introduce a stochastic picture describing the role of fluctuations in the survival of new species in non-linear systems.

Noise-induced transition from translational to rotational motion of swarms.

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.

Active and passive Brownian motion of charged particles in two-dimensional plasma models.

The dynamics of charged Coulomb grains in a plasma is numerically and analytically investigated. Analogous to recent experiments, it is assumed that the grains are trapped in an external parabolic field. Our simulations are based on a Langevin model, where the grain-plasma interaction is realized by a velocity-dependent friction coefficient and a velocity-independent diffusion coefficient.

Exact solutions for evolutionary strategies on harmonic landscapes.

In this paper two different evolutionary strategies are tested by means of harmonic landscapes. Both strategies are based on ensembles of searchers, spreading over the search space according to laws inspired by nature. The main difference between the two prototypes is given by the underlying selection mechanism, governing the increase or decrease of the local population of searchers in certain regions of the search space.

Excitation of rotational modes in two-dimensional systems of driven Brownian particles.

Models of active Brownian motion in two-dimensional (2D) systems developed earlier are investigated with respect to the influence of linear attracting forces and external noise. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. In this case an analytical study of the bifurcations of the system is possible.

Bifurcations of a semiclassical atom in a periodic field.

The dynamics of an electron moving in the Coulomb field of a nucleus and a strong periodic field is studied in a semiclassical model. Hamiltonian equations of motion are derived using Gaussian wave functions, a variational principle, and an adiabatic approximation for the width of the wave packets. Predictions for the ionization probability are found to agree rather well with exact calculations in the barrier suppression regime.

Ensemble-based control of evolutionary optimization algorithms.

This paper presents a study on how the intrinsic search parameters of an evolutionary optimization algorithm can be automatically controlled. It will be shown that only a small search parameter window ensures good optimization results. This evolutionary window, enclosing effective values for the mutation rate and temperature, can be adapted to by carefully steering the ensemble's fitness dispersion.

Entropy and complexity of finite sequences as fluctuating quantities.

The paper is devoted to the analysis of digitized sequences of real numbers and discrete strings, by means of the concepts of entropy and complexity. Special attention is paid to the random character of these quantities and their fluctuation spectrum. As applications, we discuss neural spike-trains and DNA sequences.