Related papers: Using Horseshoes to Create Coherent Structures
We show how a simple scheme of symbolic dynamics distinguishes a chaotic from a random time series and how it can be used to detect structural relationships in coupled dynamics. This is relevant for the question at which scale in complex…
We present an inverse method to construct large classes of chaotic invariant sets together with their exact statistics. The associated dynamical systems are characterized by a probability distribution and a two-form. While our emphasis is…
After early work of Henon it has become folk knowledge that symmetric periodic orbits are of particular importance. We reinforce this belief by additional studies and we further find that invariant closed symplectic submanifolds caused by…
In this paper, we mainly study the turbulence of Lagrangian flow advected by stochastic 2D Navier-Stokes equations. It is proved that this system has observable full-horseshoes. The observable full-horseshoe means that it is a kind of…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Lagrangian coherent structures are effective barriers, sticky regions, that separate phase space regions of different dynamical behavior. The usual way to detect such structures is via finite-time Lyapunov exponents. We show that similar…
The two-dimensional ideal fluid and the plasma confined by a strong magnetic field exhibit an intrinsic tendency to organization due to the inverse spectral cascade. In the asymptotic states reached at relaxation the turbulence has vanished…
By using direct numerical simulations (DNS) at unprecedented resolution we study turbulence under rotation in the presence of simultaneous direct and inverse cascades. The accumulation of energy at large scale leads to the formation of…
Chaos often represents a severe obstacle for the set-up of many-body experiments, e.g., in fusion plasmas or turbulent flows. We propose a strategy to control chaotic diffusion in conservative systems. The core of our approach is a small…
We outline the principal results of a recent examination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration. Two examples serve to illustrate the…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
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…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems…
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the…
We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition.…
We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed…
It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for…
In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…