Nonlinear resonance in an overdamped Duffing oscillator as a model of paleoclimate oscillations.

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models.

Trend analysis in the presence of short- and long-range correlations with application to regional warming.

Many real-world time series exhibit both significant short- and long-range temporal correlations. Such correlations enhance the errors of linear trend analysis. In this paper, we provide a general framework for trend analysis under the consideration of such correlations.

Complexity and transition to chaos in coupled Adler-type oscillators.

Coupled nonlinear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the subject of this contribution.

Scale-dependent error growth in Navier-Stokes simulations.

We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy simulations (LES) and direct numerical simulations of sinusoidally driven Navier-Stokes equations in three dimensions. Independent of the Reynolds number when nondimensionalized by Kolmogorov units, the LES Lyapunov exponent diverges as an inverse power of the effective grid spacing showing that the fine scale structures exhibit much faster error growth rates than the larger ones. Effectively, i.

Data-driven load profiles and the dynamics of residential electricity consumption.

The dynamics of power consumption constitutes an essential building block for planning and operating sustainable energy systems. Whereas variations in the dynamics of renewable energy generation are reasonably well studied, a deeper understanding of the variations in consumption dynamics is still missing. Here, we analyse highly resolved residential electricity consumption data of Austrian, German and UK households and propose a generally applicable data-driven load model.

Higher-order interaction learning of line failure cascading in power networks.

Line failure cascading in power networks is a complex process that involves direct and indirect interactions between lines' states. We consider the inverse problem of learning statistical models to find the sparse interaction graph from the pairwise statistics collected from line failures data in the steady states and over time. We show that the weighted -regularized pairwise maximum entropy models successfully capture pairwise and indirect higher-order interactions undistinguished by observing the pairwise statistics.

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes.

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function.

Time reversal symmetry and the difference between relaxations and building-up periods.

Autocorrelations in stationary systems are time-symmetric, irrespective of the signal's properties. Linear dynamics is usually associated with signals which are statistically time inversion invariant. This is known to be broken for non-Gaussian models.

Role of thermal fluctuations in biological copying mechanisms.

During transcription, translation, or self-replication of DNA or RNA, information is transferred to the newly formed species from its predecessor. These processes can be interpreted as (generalized) biological copying mechanism as the new biological entities like DNA, RNA, or proteins are representing the information of their parent bodies uniquely. The accuracy of these copying processes is essential, since errors in the copied code can reduce the functionality of the next generation.

Characterizing variability and predictability for air pollutants with stochastic models.

We investigate the dynamics of particulate matter, nitrogen oxides, and ozone concentrations in Hong Kong. Using fluctuation functions as a measure for their variability, we develop several simple data models and test their predictive power. We discuss two relevant dynamical properties, namely, the scaling of fluctuations, which is associated with long memory, and the deviations from the Gaussian distribution.

On star-convex volumes in 2-D hydrodynamical flows and their relevance for coherent transport.

Oceanic surface flows are dominated by finite-time mesoscale structures that separate two-dimensional flows into volumes of qualitatively different dynamical behavior. Among these, the transport boundaries around eddies are of particular interest since the enclosed volumes show a notable stability with respect to filamentation while being transported over significant distances with consequences for a multitude of different oceanic phenomena. In this paper, we present a novel method to analyze coherent transport in oceanic flows.

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions.

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network.

Evolution and transformation of early modern cosmological knowledge: a network study.

We investigated the evolution and transformation of scientific knowledge in the early modern period, analyzing more than 350 different editions of textbooks used for teaching astronomy in European universities from the late fifteenth century to mid-seventeenth century. These historical sources constitute the Sphaera Corpus. By examining different semantic relations among individual parts of each edition on record, we built a multiplex network consisting of six layers, as well as the aggregated network built from the superposition of all the layers.

Stochastic resonance and hysteresis in climate with state-dependent fluctuations.

We consider two aspects in climatic science where bistability between the two stable states of the systems is observed. One is the transition between the glacial and the interglacial period in Earth's glacial cycle. Another is the thermohaline circulation in the North Atlantic ocean.

Probabilistic properties of detrended fluctuation analysis for Gaussian processes.

Detrended fluctuation analysis (DFA) is one of the most widely used tools for the detection of long-range dependence in time series. Although DFA has found many interesting applications and has been shown to be one of the best performing detrending methods, its probabilistic foundations are still unclear. In this paper, we study probabilistic properties of DFA for Gaussian processes.

Identifying characteristic time scales in power grid frequency fluctuations with DFA.

Frequency measurements indicate the state of a power grid. In fact, deviations from the nominal frequency determine whether the grid is stable or in a critical situation. We aim to understand the fluctuations of the frequency on multiple time scales with a recently proposed method based on detrended fluctuation analysis.

Apparent violations of the second law in two-level systems.

We examine two-level systems which undergo an instantaneous change in the energy level differences due to the application of an external protocol. In particular the behavior of the work distribution as well as the probability of second-law violations as the thermodynamic limit, and separately the quasistatic limit, is approached are investigated.

Logical response induced by temperature asymmetry.

It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths.

Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average.

We present a bottom-up derivation of fluctuation analysis with detrending for the detection of long-range correlations in the presence of additive trends or intrinsic nonstationarities. While the well-known detrended fluctuation analysis (DFA) and detrending moving average (DMA) were introduced ad hoc, we claim basic principles for such methods where DFA and DMA are then shown to be specific realizations. The mean-squared displacement of the summed time series contains the same information about long-range correlations as the autocorrelation function but has much better statistical properties for large time lags.

Large-deviation probabilities for correlated Gaussian processes and intermittent dynamical systems.

In its classical version, the theory of large deviations makes quantitative statements about the probability of outliers when estimating time averages, if time series data are identically independently distributed. We study large-deviation probabilities (LDPs) for time averages in short- and long-range correlated Gaussian processes and show that long-range correlations lead to subexponential decay of LDPs. A particular deterministic intermittent map can, depending on a control parameter, also generate long-range correlated time series.

An extended transfer operator approach to identify separatrices in open flows.

Vortices of coherent fluid volume are considered to have a substantial impact on transport processes in turbulent media. Yet, due to their Lagrangian nature, detecting these structures is highly nontrivial. In this respect, transfer operator approaches have been proven to provide useful tools: Approximating a possibly time-dependent flow as a discrete Markov process in space and time, information about coherent structures is contained in the operator's eigenvectors, which is usually extracted by employing clustering methods.

Early warning signal for interior crises in excitable systems.

The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and nonbifurcation-type transitions. We extend this toolbox and report on a characteristic scaling behavior (critical attractor growth) which is indicative of an impending global bifurcation, an interior crisis in excitable systems.

Scale-invariant Green-Kubo relation for time-averaged diffusivity.

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time- and ensemble-averaged mean-squared displacement are remarkably different. The ensemble-averaged diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale-invariant nonstationary velocity correlation function with the transport coefficient. Here we obtain the relation between time-averaged diffusivity, usually recorded in single-particle tracking experiments, and the underlying scale-invariant velocity correlation function.

Infinite invariant densities due to intermittency in a nonlinear oscillator.

Dynamical intermittency is known to generate anomalous statistical behavior of dynamical systems, a prominent example being the Pomeau-Manneville map. We present a nonlinear oscillator, i.e.

Anomalous diffusion on a fractal mesh.

We present exact analytical results for properties of anomalous diffusion on a fractal mesh. The fractal mesh structure is a direct product of two fractal sets, one belonging to a main branch of backbones, the other to the side branches of fingers. Both fractal sets are constructed on the entire (infinite) y and x axes.