Concept

Lissajous orbit

Related publications (11)

Constructing periodic orbits of high-dimensional chaotic systems by an adjoint-based variational method

Tobias Schneider, Sajjad Azimi, Omid Ashtari

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...

2022

Invariant tori in dissipative hyperchaos

Tobias Schneider, Jeremy Peter Parker

One approach to understand the chaotic dynamics of nonlinear dissipative systems is the study of non-chaotic yet dynamically unstable invariant solutions embedded in the system's chaotic attractor. The significance of zero-dimensional unstable fixed points ...

AIP Publishing2022

Variational methods for finding periodic orbits in the incompressible Navier Stokes equations

Tobias Schneider, Jeremy Peter Parker

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, bas ...

CAMBRIDGE UNIV PRESS2022

Periodic orbits exhibit oblique stripe patterns in plane Couette flow

Tobias Schneider, Florian Reetz

Spatiotemporally chaotic dynamics of transitional plane Couette flow may give rise to regular turbulent-laminar stripe patterns with a large-scale pattern wavelength and an oblique orientation relative to the laminar flow direction. A recent dynamical syst ...

AMER PHYSICAL SOC2021

Fully automated gridding reconstruction for non-Cartesian x-space magnetic particle imaging

Ahmet Alacaoglu

Magnetic particle imaging (MPI) is a fast emerging biomedical imaging modality that exploits the nonlinear response of superparamagnetic iron oxide (SPIO) nanoparticles to image their spatial distribution. Previously, various scanning trajectories were ana ...

2019

Exponentially long orbits in Hopfield neural networks

Wulfram Gerstner, Johanni Michael Brea, Samuel Pavio Muscinelli

We show that Hopfield neural networks with synchronous dynamics and asymmetric weights admit stable orbits that form sequences of maximal length. For N units, these sequences have length T = 2^N; that is, they cover the full state space. We present a mathe ...

Massachusetts Institute of Technology Press2017

Cosmology From Gravitational Lens Time Delays And Planck Data

Frédéric Courbin, Georges Meylan, Malte Tewes

Under the assumption of a flat Lambda CDM cosmology, recent data from the Planck satellite point toward a Hubble constant that is in tension with that measured by gravitational lens time delays and by the local distance ladder. Prosaically, this difference ...

Iop Publishing Ltd2014

Unstable periodic orbits in the Lorenz attractor

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than ...

2011

New variational principles for locating periodic orbits of differential equations

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerica ...

2011

Autoregressive moving average model for analyzing edge localized mode time series on Axially Symmetric Divertor Experiment (ASDEX) Upgrade tokamak

Hartmut Zohm

An approach to analysis of time series of edge localized modes (ELMs) is proposed. It is based on the use of the autoregressive moving average model, which decomposes time series into deterministic and noise components. Despite the inclusion of nonlinearit ...

2004

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