On the chaotic dynamics of a modified Nose-Hoover oscillator

This article reports on a study of the two-dimensional parameter space of a generalized time-reversible Nos´e-Hoover oscillator. Instead of considering its original form, whose study of the one-dimensional parameter space has recently received new insights, we examine the Nos´e-Hoover model slightly modified by using a new parameter (cid:15) 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 (cid:15) and (ii) the effect of higher values of (cid:15) . It is shown that, for higher values of the new dissipative parameter (cid:15) , the existence of chaotic behavior only prevails for the backwards dynamics.