NoseHoover

Systems / ODEs / Chaotic attractors

A conservative thermostatted oscillator — chaos without dissipation, sampling a canonical ensemble.

continuous · ODE3 dimensionsconservative

Interactive: drag to rotate

Definition

\[ \begin{aligned} \dot{y_{0}} &= y_{1} \\ \dot{y_{1}} &= - y_{0} + y_{1} y_{2} \\ \dot{y_{2}} &= a - y_{1}^{2} \end{aligned} \]

Parameters

Symbol	Default	Role
a	1.5	target-temperature parameter of the thermostat

Properties

Lyapunov spectrum

$-0.01606,\; -0.01133,\; +0.009012$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 1.795$

Divergence ∇·f

$\nabla\!\cdot f = y_{2}$
state-dependent

Equilibria

none found (no equilibria)

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.NoseHoover()
traj = sys.integrate(final_time=100.0, dt=0.01)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference

Nosé (1984), J. Chem. Phys. 81, 511-519; Hoover (1985), Phys. Rev. A 31, 1695-1697

BibTeX

@misc{nosehoover,
  title = {NoseHoover system},
  note = {Nosé (1984), J. Chem. Phys. 81, 511-519; Hoover (1985), Phys. Rev. A 31, 1695-1697}
}