Impulsive coupling between two anharmonic oscillators: a kicked rotor paradigm

Impulsive coupling between two anharmonic oscillators is the sporadic, rapid transition from one type of oscillatory dynamics to another. The cause of these impulsive transitions is elucidated by mapping the Hamiltonian of the coupled anharmonic oscillators to an expression for the total energy of a non-rigid asymmetric rotor. Trajectories of the rotor angular momentum vector are displayed on a rotational energy surface and are classified by a separatrix that separates the rotor phase space into three regions. Each region corresponds to qualitatively dissimilar oscillator dynamics, and the separatrix corresponds to a barrier that hinders the transition between the different types of oscillatory dynamics. In certain zones of rotor phase space, a "kick", identified as a particular part of the coupling between the two oscillators, drives the angular momentum vector across the separatrix, thereby reproducing the essential features of impulsive coupling.