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Variants of the Nosé–Hoover oscillator

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Abstract

The Nosé–Hoover oscillator is a well-studied chaotic system originally proposed to model a harmonic oscillator in equilibrium with a heat bath at constant temperature. Although it is a simple three-dimensional system with five terms and two quadratic nonlinearities, it displays a rich variety of unusual dynamics, but it falls considerably short of its original purpose. This review describes two simple variants of the Nosé–Hoover oscillator, the first of which satisfies the original goal exactly, and the second of which exhibits a hidden global chaotic attractor that fills all of its three-dimensional state space.

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  1. Department of Physics, University of Wisconsin – Madison, Madison, WI, 53706, USA

    J. C. Sprott

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  1. J. C. Sprott
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Correspondence to J. C. Sprott.

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Sprott, J.C. Variants of the Nosé–Hoover oscillator. Eur. Phys. J. Spec. Top. 229, 963–971 (2020). https://doi.org/10.1140/epjst/e2020-900163-1

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