On the chaotic dynamics of a modified Nosé-Hoover oscillator

Abstract

This article reports on a study of the two-dimensional parameter space of a generalized time-reversible Nosé-Hoover oscillator. Instead of considering its original form, whose study of the one-dimensional parameter space has recently received new insights, we examine the Nosé-Hoover model slightly modified by using a new parameter ε to introduce a dissipative term to its energizing-damping variable. We use the maximum Lyapunov exponent to numerically characterize the chaotic dynamics of the model, at representative points of the two- dimensional parameter space, treating separately two dynamical regimes resulting from: (i) the effect of lower values of ε and (ii) the effect of higher values of ε. It is shown that, for higher values of the new dissipative parameter ε, the existence of chaotic behavior only prevails for the backwards dynamics.