Variants of the Nose–Hoover oscillator

J.C. Sprott
Department of Physics, University of Wisconsin - Madison, Madison, WI 53706, USA

Received 5 August 2019 Published online 26 March 2020

The Nose–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 Nose–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.

Ref: J. C. Sprott, European Physical Journal Special Topics 229, 963-971 (2020).

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