Time-dependent generalization of the Nos-Hoover thermostatting technique for molecular dynamics simulations

The Nosé-Hoover scheme demonstrates that molecular dynamics simulations can be used to calculate the properties of systems at constant temperature (i.e. canonical ensemble averages). There is interest in deterministic generalizations of Nosé-Hoover dynamics which are ergodic even for simple systems like the harmonic oscillator. Prompted by parallels with studies of the Duffing oscillator within control theory, we have investigated a non-autonomous version of the Nosé-Hoover oscillator in which the temperature is replaced by a weakly time-dependent function. This function is chosen so that its average over time coincides with the temperature desired. Calculations are facilitated by graphical programming with a MATLAB-Simulink platform. A time series analysis of our simple non-autonomous system yields the position and momentum distributions expected for the harmonic oscillator.