Related papers: Applications of Dynamical Systems in Engineering
Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry, and partly from…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
While there have been many publications on potential applications of chaos to fields such as communications, radar, sonar, random signal generation, channel equalization and others, designing continuous chaotic systems is still an unsolved…
The universal dynamic uncertainty, discovered in Parts I and II of this series of papers for the case of Hamiltonian quantum systems, is further specified to reveal the hierarchical structure of levels of dynamically redundant…
Grids - the collection of heterogeneous computers spread across the globe - present a new paradigm for the large scale problems in variety of fields. We discuss two representative cases in the area of condensed matter physics outlining the…
A three-component dynamic system with influence of pumping and nonlinear dissipation describing a quantum cavity electrodynamic device is studied. Different dynamical regimes are investigated in terms of divergent trajectories approaches…
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems,…
In this paper we present an approach in which synchronization of chaos is used to address identification problems. In particular, we are able to identify: (i) the discontinuity points of systems described by piecewise dynamical equations…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
Deep learning has been the most popular machine learning method in the last few years. In this chapter, we present the application of deep learning and physics-informed neural networks concerning structural mechanics and vibration problems.…
Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term macroscale dynamics from detailed microscale dynamics. We explore such coordinate…
A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting…
We review the properties of fractals, the Mandelbrot set and how deterministic chaos ties to the picture. A detailed study on three body systems, one of the major applications of chaos theory was undertaken. Systems belonging to different…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified…