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Some simple chaotic flows

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · 1994 · Vol. 50(2) · pp. R647–R650

J. C. Sprott✉(University of Wisconsin–Madison)

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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.

Chaos control and synchronization Quantum chaos and dynamical systems Complex Systems and Time Series AnalysisLyapunov exponentChaoticSimple (philosophy)Nonlinear systemQuadratic equationOrdinary differential equationStatistical physicsFractalChaotic mixingChaotic scattering

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Elementary quadratic chaotic flows with no equilibria