相关论文: Remarks on Power Spectra of Chaotic Dynamical Syst…

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…

We solve the problem of resonance statistics in systems with broken time-reversal invariance by deriving the joint probability density of all resonances in the framework of a random matrix approach and calculating explicitly all n-point…

A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…

We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate…

Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…

We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions…

This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic…

In this work, we explore a numerical approach for performing the inverse Laplace transformation, with an emphasis on achieving stability and robustness under noisy conditions. Our quadrature-based method integrates reparameterization, data…

We are interested in time series of the form $y_{n} = x_{n} + \xi_{n}$ where ${x_{n}}$ is generated by a chaotic dynamical system and where $\xi_{n}$ models observational noise. Using concentration inequalities, we derive fluctuation bounds…

Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Atmospheric flows exhibit long-range spatiotemporal correlations manifested as the fractal geometry to the global cloud cover pattern concomitant with inverse power-law form for power spectra of temporal fluctuations of all scales ranging…

We study correlations of the amplitudes of wave functions of a chaotic system at large distances. For this purpose, a joint distribution function of the amplitudes at two distant points in a sample is calculated analytically using the…

We analytically determine the correlation functions of the stochastic response of a generic mapping system driven by colored noise. We also address the issue of noise cascading in coupled-element systems, particularly in a uni-directionally…

We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…

A recently proposed technique correlating electric fields and particle velocity distributions is applied to single-point time series extracted from linearly unstable, electrostatic numerical simulations. The form of the correlation, which…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

In this work, we show that the inverse-$\lambda$ shape in the fundamental diagram of traffic flow can be produced dynamically by a simple nonlinear mesoscopic model with stochastic noises. The proposed model is based on the gas-kinetic…

We propose a new method for determining the stochastic or ordered nature of trajectories in non-integrable Hamiltonian dynamical systems. The method consists of constructing a time-series from the divergence of nearby trajectories and then…