相关论文: Recurrence Plot Based Measures of Complexity and i…

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…

Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…

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…

Ordinal measures provide a valuable collection of tools for analyzing correlated data series. However, using these methods to understand the information interchange in networks of dynamical systems, and uncover the interplay between…

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…

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example,…

Ultra-large scale (ULS) systems are becoming pervasive. They are inherently complex, which makes their design and control a challenge for traditional methods. Here we propose the design and analysis of ULS systems using measures of…

This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…

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…

We present a novel approach to learn the formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a statistical dynamical model of the system which…

The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical…

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 review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…

Heteroscedasticity -- where the variance of a variable changes with other variables -- is pervasive in real data, and elucidating why it arises from the perspective of statistical moments is crucial in scientific knowledge discovery and…

We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…

We apply measures of complexity, emergence and self-organization to an abstract city traffic model for comparing a traditional traffic coordination method with a self-organizing method in two scenarios: cyclic boundaries and non-orientable…

Many types of ventricular and atrial cardiac arrhythmias have been discovered in clinical practice in the past 100 years, and these arrhythmias are a major contributor to sudden cardiac death. Ventricular tachycardia, ventricular…