Related papers: Can averaged orbits be used to extract scaling fun…
The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…
We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
For a general class of diffusion processes with multiplicative noise, describing a variety of physical as well as financial phenomena, mostly typical of complex systems, we obtain the analytical solution for the moments at all times. We…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
The recent paper claims that mean characteristics of chaotic orbits differ from the corresponding values averaged over the set of unstable periodic orbits, embedded in the chaotic attractor. We demonstrate that the alleged discrepancy is an…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…
Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making…
One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters.…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…