Related papers: Computing Chaotic Time-Averages from Few Periodic …
This paper continues a numerical investigation of orbits evolved in `frozen,' time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…
Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as…
By computing 254 unstable stationary solutions of the Kuramoto-Sivashinsky equation in the extensive chaos regime (Lyapunov fractal dimension D=8.8), we find that 30% satisfy the symmetry of the time-average pattern of the spatiotemporal…
We suggest a method to compute approximations to temporal correlation functions of few-body observables in chaotic many-body systems in the thermodynamic limit based on the respective Lanczos coefficients. Given the knowledge of these…
We examine the effect of short unstable periodic orbits on wavefunction statistics in a classically chaotic system, and find that the tail of the wavefunction intensity distribution in phase space is dominated by scarring associated with…
We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…
We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series…
Predictive Feedback Control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive Feedback Control is severely limited because asymptotic convergence speed decreases with…
The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
It is a well established result that, in classical dynamical systems with sufficient time-scale separation, the fast chaotic degrees of freedom are well modeled by (Gaussian) white noise. In this paper, we present the stochastic dynamical…
The application of random matrix theory to scattering requires introduction of system-specific information. This paper shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically…
This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…
We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from…
We use a simple dynamical model in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central, spherically symmetric, dense nucleus and a flat disk. In particular, we explore how the total orbital…
We use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour. Our approach to circumvent the lack of precise models for some…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…