Some simple chaotic flows

1994/08/01 by J. C. Sprott · 7 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Quantum chaos and dynamical systems

paper · doi:10.1103/physreve.50.r647

openalex publication_date 1994/08/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

A systematic examination of general three-dimensional autonomous ordinary differential equations with quadratic nonlinearities has uncovered 19 distinct simple examples of chaotic flows with either five terms and two nonlinearities or six terms and one nonlinearity. The properties of these systems are described, including their critical points, Lyapunov exponents, and fractal dimensions.

Citations

• Deterministic Nonperiodic Flow
• Determining Lyapunov exponents from a time series

Cited by

• A non-autonomous conservative system and its reconstitution in integral domain
• Modelings and mechanism analysis underlying both the 4D Euler equations and Hamiltonian conservative chaotic systems
• Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo
• Dynamical Alignment: A Principle for Adaptive Neural Computation
• Storage and recall of multiple chaotic attractors in minimal reservoir computers
• Hidden attractors in dynamical systems
• Structure analysis of the Lorenz-84 chaotic attractor

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