相关论文: Using the Magnitude-Squared Coherence for Determin…
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Uncertainty quantification techniques such as the time-dependent generalized polynomial chaos (TD-gPC) use an adaptive orthogonal basis to better represent the stochastic part of the solution space (aka random function space) in time.…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
The spectral statistic $\delta_n$ measures the fluctuations of the number of energy levels around its mean value. It has been shown that chaotic quantum systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the $\delta_n$…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial…
We present a new method for locating unstable periodic points of one dimensional chaotic maps. This method is based on order statistics. The densities of various maxima of the iterates are discontinuous exactly at unstable periodic points…
This work mainly investigates the mean-square stability and stabilizability for a single-input single-output networked linear feedback system. The control signal in the networked system is transmitted over an unreliable channel. In this…
We introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called…
In the study of subdiffusive wave-packet spreading in disordered Klein-Gordon (KG) nonlinear lattices, a central open question is whether the motion continues to be chaotic despite decreasing densities, or tends to become quasi-periodic as…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
A new approach is proposed to the quantitative estimation of the complexity of multidimensional discrete sequences in terms of the shapes of their trajectories in the extended space of states. This approach is based on the study of the…
In this work it is shown that dynamical quantum phase transitions in Loschmidt echos control the nonequilibrium dynamics of the order parameter after particular quantum quenches in systems with broken-symmetry phases. A direct connection…
In this paper, we introduce a novel method to identify transitions from steady states to chaos in stochastic models, specifically focusing on the logistic and Ricker equations by leveraging the gamma distribution to describe the underlying…
This work presents a sum-of-squares (SOS) based framework to perform data-driven stabilization and robust control tasks on discrete-time linear systems where the full-state observations are corrupted by L-infinity bounded input,…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
This paper proposes a novel load frequency control (LFC) approach formulated on an optimal structure of the coefficient diagram method (CDM) in a two-area thermal power system. As part of a realistic analysis, nonlinearities related to…