Related papers: Characterizations of model sets by dynamical syste…

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…

We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…

A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…

Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…

Model sets are always Meyer sets but the converse is generally not true. In this work we show that for a repetitive Meyer multiple sets of $\mathbb{R}^d$ with associated dynamical system $(\mathbb{X}, \mathbb{R}^d)$, the property of being a…

Given a linear time-periodic control system in a Hilbert space with a bounded control operator, we present a characterization of periodic stabilization in terms of a detectability inequality. Similar characterizationwas built up in [E.…

We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…

Although models are built on the basis of some observations of reality, the concepts that derive theoretically from their definitions as well as from their characteristics and properties are not necessarily direct consequences of these…

This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…

We investigate the stability properties of two different classes of metabolic cycles using a combination of analytical and computational methods. Using principles from structural kinetic modeling (SKM), we show that the stability of…

In principle, all the natural systems such as biological, ecological and economical systems are structure-variable systems (in which some environment parameters are not fixed). In this Letter we show that data sequences from many…

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…

This paper investigates the identification of quantiles and quantile regression parameters when observations are set valued. We define the identification set of quantiles of random sets in a way that extends the definition of quantiles for…

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…

We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…

Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…