Measuring chaos in the Lorenz and Rössler models: fidelity tests for reservoir computing

DOI10.1063/5.0065044zbMath1546.3715MaRDI QIDQ6556965

James Scully, Alexander B. Neiman, Andrej L. Shil'nikov

Publication date: 17 June 2024

Published in: Chaos (Search for Journal in Brave)

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Numerical chaos (65P20) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Cites Work

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• A Mathematical Theory of Communication
• Pseudohyperbolicity and the problem on periodic perturbations of Lorenz-type attractors
• Word frequency and entropy of symbolic sequences: A dynamical perspective
• On models with non-rough Poincaré homoclinic curves
• Finite sample effects in sequence analysis
• Prediction and entropy of nonlinear dynamical systems and symbolic sequences with LRO
• Quasiattractors and homoclinic tangencies
• Correlation analysis of dynamical chaos
• (INVITED) Homoclinic puzzles and chaos in a nonlinear laser model
• An equation for continuous chaos
• Scientific heritage of L. P. Shilnikov
• SYMBOLIC DYNAMICS, COARSE GRAINING AND THE MONITORING OF COMPLEX SYSTEMS
• Symbolic Quest into Homoclinic Chaos
• Julia: A Fresh Approach to Numerical Computing
• An inequality for the entropy of differentiable maps
• Compression of individual sequences via variable-rate coding
• An example of a wild strange attractor
• Ergodic theory of chaos and strange attractors
• Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data
• Nonlinear time-series analysis revisited
• Nonlinear Time Series Analysis
• Wild pseudohyperbolic attractor in a four-dimensional Lorenz system
• Ordered intricacy of Shilnikov saddle-focus homoclinics in symmetric systems
• Homoclinic chaos in the Rössler model

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