Performance analysis of indicators of chaos for nonlinear dynamical systems

Abstract

The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the performance of chaos detection by means of numerical simulations. The challenge is to predict chaotic behavior based on the analysis of orbits of limited length. In this paper, the performance analysis of past and recent indicators of chaos, in terms of predictive power, is carried out in detail using the dynamical system characterized by a symplectic Hénon-like cubic polynomial map.

References in corpus (10)

• Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
• Characteristic distributions of finite-time Lyapunov exponents
• Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
• Super convergence of ergodic averages for quasiperiodic orbits
• Detecting chaos in particle accelerators through the frequency map analysis method
• Diffusion and scaling in escapes from two-degree-of-freedom Hamiltonian systems
• Quantitative Quasiperiodicity
• The Reversibility Error Method (REM): a new, dynamical fast indicator for planetary dynamics
• Aplication of Frequency Map Analysis to Beam-Beam Effects Study in Crab Waist Collision Scheme
• Refined betatron tune measurements by mixing beam position data

Cited by in corpus (12)

• Kinetic versus Magnetic Chaos in Toroidal Plasmas: A systematic quantitative comparison
• Resonance and Weak Chaos in Quasiperiodically-Forced Circle Maps
• Approximate Entropy Analysis for Nonlinear Beam Dynamics
• Online regularization of Poincaré map of storage rings with Shannon entropy
• Construction of approximate invariants for non-integrable Hamiltonian systems
• Efficient detection of chaos through the computation of the Generalized Alignment Index (GALI) by the multi-particle method
• Breather bound states in a parametrically driven magnetic wire
• Computing Lyapunov Exponents using Weighted Birkhoff Averages
• Sextupole reduction via chaos suppression at the National Synchrotron Light Source II
• Geometry of Almost-Conserved Quantities in Symplectic Maps. Part I: Perturbation Theory
• Geometry of Almost-Conserved Quantities in Symplectic Maps. Part II: Recovery of approximate invariant
• Isochronous and period-doubling diagrams for symplectic maps of the plane