Simple estimation method for the second-largest Lyapunov exponent of chaotic differential equations

DOI10.1016/j.chaos.2020.109981zbMath1490.37106OpenAlexW3037216209WikidataQ115359224 ScholiaQ115359224MaRDI QIDQ2122938

Shuang Zhou, Xing-Yuan Wang

Publication date: 7 April 2022

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2020.109981

zbMATH Keywords

chaoschaotic differential equationssecond-largest Lyapunov exponent

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimation of the largest Lyapunov exponent from the perturbation vector and its derivative dot product
• Lyapunov-type stability and Lyapunov exponent for exemplary multiplicative dynamical systems
• Jacobian matrix algorithm for Lyapunov exponents of the discrete fractional maps
• SVD algorithms to approximate spectra of dynamical systems
• Determining Lyapunov exponents from a time series
• Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. I: Theory
• Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems
• An efficient QR based method for the computation of Lyapunov exponents
• The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map
• Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm
• Proposing a two-level stochastic model for epileptic seizure genesis
• On the use of interval extensions to estimate the largest Lyapunov exponent from chaotic data
• Output formation-containment of interacted heterogeneous linear systems by distributed hybrid active control
• Image encryption algorithm for synchronously updating Boolean networks based on matrix semi-tensor product theory
• Exponential stability of singularly perturbed switched systems with all modes being unstable
• Fast image encryption algorithm based on parallel computing system
• A practical method for calculating largest Lyapunov exponents from small data sets
• A local echo state property through the largest Lyapunov exponent
• Numerical Analysis and Improved Algorithms for Lyapunov-Exponent Calculation of Discrete-Time Chaotic Systems
• A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions
• Ergodic theory of chaos and strange attractors
• Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
• Deterministic Nonperiodic Flow
• A novel method based on the pseudo-orbits to calculate the largest Lyapunov exponent from chaotic equations
• 3D Grid Multi-Wing Chaotic Attractors
• Optimal Persistent Monitoring Using Second-Order Agents With Physical Constraints
• Estimating Lyapunov exponents in billiards

This page was built for publication: Simple estimation method for the second-largest Lyapunov exponent of chaotic differential equations