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. This is because the intrinsic noise in the experimental setup remains constant as it is not affected by the scale factor. The particular case considered here offers a genuine noise-level effect in significantly altering a period-doubling cascade to chaos besides producing an expected truncated cascade. By monitoring with increasing value a significant parameter in the dynamics of the problem when searching for its solution, the system alien to the noise (or better said with a negligible noise level) follows a period-doubling cascade from period one to period two to period four to period eight and, eventually, chaos. However, if the intrinsic noise strength significantly enters the evolution, there appears a parallel sequence of period doublings different from the one found in the previous case.

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. None of these properties hold in the general Lévy case. Thus, the level lines of the joint probability density are not elliptic. The coordinate and the velocity of the oscillator are strongly dependent, and this dependence is quantified by introducing the corresponding parameter ("width deficit"). The distribution of the phase is inhomogeneous and highly nontrivial.

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.

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). In the presence of an external electric field we obtain the current-field characteristics for a wide range of values of all parameters defining the system. Finally, we discuss the conditions for an Ohmic-non-Ohmic transition of the electric current as the electric field strength is varied.

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. In particular we consider the fate of new species with non-linear growth. As an application of the general model framework we consider the fate of 'rare species' in early biological evolution. We show that hypercycle systems do not represent the end of the evolutionary process as they may evolve further in small niches. This has implications for different types of applications ranging from biological systems on one level to socio-technological systems on a more metaphoric level.

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. In addition to the ordinary case of positive (passive) friction between grains and plasma, we also discuss the effects of negative (active) friction. The latter case seems particularly interesting, since recent analytical calculations have shown that friction coefficients with negative parts may appear in some models of ion absorption by grains as well as in models of ion-grain scattering. Such negative friction may cause active Brownian motions of the grains. As our computer simulations show, the influence of negative friction leads to the formation of various stationary modes (rotations, oscillations), which, to some extent, can also be estimated analytically.

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. More precisely, we compare a thermodynamic strategy, which is based on a physically motivated local selection criterion, with a biologically motivated strategy, which features a global selection scheme (i.e., global coupling of the searchers). Confining ourselves to a special class of initial conditions, we show that, in the simple case of harmonic test potentials, both strategies possess particular analytical solutions of the same type. By means of these special solutions, the velocities of the two strategies can be compared exactly. In the last part of the paper, we extend the scope of our discussion to a mixed strategy, combining local and global selection.

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. We show that in the presence of external linear forces with only small deviations from radial symmetry, the system develops rotational excitations with left-right symmetry, corresponding to limit cycles in the 4D phase space, the corresponding distribution has the form of a hoop or a tire in the 4D space. In the last part we apply the theory to swarms of Brownian particles that are held together by weak and attracting forces, which lead to cluster formation. Since near the center the potential is at least approximately parabolic and near to the radial symmetry, the swarm develops rotational modes of motion with left-right symmetry.

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. A control sensor based on an entropy measure is introduced to achieve this goal. The efficiency of the proposed control method will be tested by optimizing artificial sequences such as the well-known low autocorrelated binary strings and natural sequences including RNA.

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. By introducing dissipation and fluctuation the model atom is considered as an open system. For the dissipative system we investigate the bifurcations in dependence on strength and frequency of the external field. A quite complex bifurcation scenario is obtained. The sensitivity with respect to noise is also studied.

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. We consider a given sequence as one realization of finite length of certain random process. The other members of the ensemble are defined by appropriate surrogate sequences and surrogate processes. We show that n-gram entropies and the context-free grammatical complexity have to be considered as fluctuating quantities and study the corresponding distributions. Different complexity measures reveal different aspects of a sequence. Finally, we show that the diversity of the entropy (that takes small values for pseudorandom strings) and the context-free grammatical complexity (which takes large values for pseudorandom strings) give, nonetheless, consistent results by comparison of the ranking of sample sequences taken from molecular biology, neuroscience, and artificial control sequences.