Variants of the Nosé–Hoover oscillator

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 unu...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2020-03, Vol.229 (6-7), p.963-971
Main Author: Sprott, J. C.
Format: Article
Language:English
Subjects:
Atomic
Chaos theory
Classical and Continuum Physics
Condensed Matter Physics
Harmonic oscillators
Materials Science
Measurement Science and Instrumentation
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Special Chaotic Systems
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Summary: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.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2020-900163-1