Related papers: Initial Conditions for Models of Dynamical Systems
It is shown how regular model sets can be characterized in terms of regularity properties of their associated dynamical systems. The proof proceeds in two steps. First, we characterize regular model sets in terms of a certain map $\beta$…
Complex systems are ubiquitous in nature and engineering, but their analysis and control are hampered by their high dimensionality and the influence of various factors on their dynamics. Dimensionality reduction aims to find a…
In this work a state transformation is presented that transforms a given state-space system to a normal form related to mechanical systems. The underlying state-space system must meet certain requirements such that a transformation exist.…
We review a dynamical approach to non-equilibrium MD (D-NEMD). We show how, using a proper simulation setup, is possible to treat interesting cases in which the initial condition is a stationary non-equilibrium state produced by a suitable…
The dynamics of many-body systems can often be captured in terms of only a few relevant variables. Mathematical and numerical approaches exist to identify these variables by exploiting a separation of time scales between slow relevant and…
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…
It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted…
Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
From some observations on economic behaviors, in particular changing economic conditions with time and space, we develop a very simple model for the evolution of economic entities within a geographical type of framework. We raise a few…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We propose a combination of cluster analysis and stochastic process analysis to characterize high-dimensional complex dynamical systems by few dominating variables. As an example, stock market data are analyzed for which the dynamical…
In standard treatments of open quantum systems, the reduced dynamics is described starting from the assumption that the system and the environment are initially uncorrelated. This assumption, however, is not always guaranteed in realistic…
Learning controllers from data for stabilizing dynamical systems typically follows a two step process of first identifying a model and then constructing a controller based on the identified model. However, learning models means identifying…
An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as…
A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…
Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
In this paper we consider the problem of controlling the dynamic behavior of a multi-robot system while interacting with the environment. In particular, we propose a general methodology that, by means of locally scaling inter-robot coupling…