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Related papers: Collective Lyapunov modes

200 papers

We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of…

Chaotic Dynamics · Physics 2009-02-24 Hong-liu Yang , Kazumasa A. Takeuchi , Francesco Ginelli , Hugues Chaté , Günter Radons

New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…

Optimization and Control · Mathematics 2019-05-17 Igor Furtat

Hybrid dynamical systems exhibit a diverse array of stability phenomena, each currently addressed by separate Lyapunov-like results. We show that these results are all instances of a single theorem: a Lyapunov function is a morphism from a…

Category Theory · Mathematics 2026-04-08 Joe Moeller , Aaron D. Ames

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…

Chaotic Dynamics · Physics 2015-05-18 Yossi Ben Zion , Lawrence Horwitz

Lagrangian chaos is experimentally investigated in a convective flow by means of Particle Tracking Velocimetry. The Fnite Size Lyapunov Exponent analysis is applied to quantify dispersion properties at different scales. In the range of…

Chaotic Dynamics · Physics 2009-11-07 G. Boffetta , M. Cencini , S. Espa , G. Querzoli

We investigate the geometrical structure of instabilities in the two-scales Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of the full spectrum of covariant Lyapunov vectors reveals the presence of a slow bundle…

Chaotic Dynamics · Physics 2019-05-22 Mallory Carlu , Francesco Ginelli , Valerio Lucarini , Antonio Politi

Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that…

Nuclear Theory · Physics 2009-10-30 Dario Vretenar , Peter Ring , Georgios A. Lalazissis , Wolfgang Poeschl

This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…

Systems and Control · Electrical Eng. & Systems 2019-06-24 Kunal Garg , Dimitra Panagou

We provide a distributed coordinated approach to the stability analysis and control design of large-scale nonlinear dynamical systems by using a vector Lyapunov functions approach. In this formulation the large-scale system is decomposed…

Dynamical Systems · Mathematics 2015-07-22 Soumya Kundu , Marian Anghel

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…

General Relativity and Quantum Cosmology · Physics 2016-08-31 C. Dettmann , N. Frankel , N. Cornish

Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing…

Chaotic Dynamics · Physics 2017-03-23 William D. Fullmer , Christine M. Hrenya

We consider discrete-time dynamical systems with a linear relaxation dynamics that are driven by deterministic chaotic forces. By perturbative expansion in a small time scale parameter, we derive from the Perron-Frobenius equation the…

Classical Analysis and ODEs · Mathematics 2018-08-01 Griffin Williams , Christian Beck

Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…

Chaotic Dynamics · Physics 2016-12-21 Kenji Shinoda , Kunihiko Kaneko

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…

Optimization and Control · Mathematics 2012-06-05 Corentin Briat , Alexandre Seuret

Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…

Adaptation and Self-Organizing Systems · Physics 2022-09-13 S. Leo Kingston , Tomasz Kapitaniak , Syamal K. Dana

As a new tool to describe the behaviour of a dynamical system, we introduce the concept of "covariant Lyapunov field", i.e. a field which assigns all the components of covariant Lyapunov vectors at almost all points of the phase space. We…

Mathematical Physics · Physics 2026-01-12 Massimo Marino , Doriano Brogioli

Neutrino-neutrino refraction can lead to non-periodic flavor oscillations in dense neutrino gases, and it has been hypothesized that some solutions are chaotic in nature. This is of particular interest in the case of neutrino emission from…

High Energy Physics - Phenomenology · Physics 2014-07-16 Rasmus Sloth Hansen , Steen Hannestad

Violent relaxation (VR) is often regarded as the mechanism leading stellar systems to collisionless meta equilibrium via rapid changes in the collective potential. We investigate the role of chaotic instabilities on single particle orbits…

Astrophysics of Galaxies · Physics 2025-06-04 Simone Sartorello , Pierfrancesco Di Cintio , Alessandro Alberto Trani , Mario Pasquato

In this paper, we review state-of-the-art results on the collective behaviors for Lohe type first-order aggregation models. Collective behaviors of classical and quantum many-body systems have received lots of attention from diverse…

Dynamical Systems · Mathematics 2021-08-25 Seung-Yeal Ha , Dohyun Kim

Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…

Astrophysics of Galaxies · Physics 2025-02-04 Eduárd Illés , Dániel Jánosi , Tamás Kovács