Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics

DOI10.1016/S0167-2789(99)00169-4zbMath0963.70501MaRDI QIDQ1969878

Giuseppe Rega, Rocco Alaggio

Publication date: 25 June 2001

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

attractorsphase-lockingprimary resonancequasiperiodic transition to chaoscontinuous experimental systemdelay-embedding techniqueelastic cable/mass systemorthogonal decomposition of spatio-temporal flow

Mathematics Subject Classification ID

Experimental work for problems pertaining to mechanics of particles and systems (70-05) Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55)

Related Items (6)

Multimode Interactions in Suspended Cables ⋮ BIFURCATION AND CHAOS ANALYSIS FOR A DELAYED TWO-NEURAL NETWORK WITH A VARIATION SLOPE RATIO IN THE ACTIVATION FUNCTION ⋮ Experimental observation and characterization of chaotic properties in a driven infrared diode circuit ⋮ Dimension reduction of dynamical systems: methods, models, applications ⋮ The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview ⋮ Closed-form solutions for the symmetric nonlinear free oscillations of pyramidal trusses

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
• Chaotic attractors on a 3-torus, and torus break-up
• Phase-space analysis of bursting behavior in Kolmogorov flow
• Attractors on an N-torus: Quasiperiodicity versus chaos
• Measuring the strangeness of strange attractors
• Extracting qualitative dynamics from experimental data
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Embedology
• Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator
• Analysis of long torsional strings by proper orthogonal decomposition
• Behavior of a three-torus in truncated Navier-Stokes equations
• Three-frequency quasiperiodicity, phase locking, and the onset of chaos
• Note concerning our paper On the nature of turbulence. Commun. math. Phys. 20, 167-192 (1971)
• Turbulence and the dynamics of coherent structures. I. Coherent structures
• Dynamics of Large Scale Coupled Structural/ Mechanical Systems: A Singular Perturbation/ Proper Orthogonal Decomposition Approach
• An empirical study of the stability of periodic motion in the forced spring-pendulum
• BIFURCATIONS AND TRANSITION TO CHAOS THROUGH THREE-DIMENSIONAL TORI
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• Ergodic theory of chaos and strange attractors

This page was built for publication: Characterizing bifurcations and classes of motion in the transition to chaos through 3D-tori of a continuous experimental system in solid mechanics