Internal resonance in non-linear disk oscillations and the amplitude
  evolution of neutron star kilohertz QPOs
  We explore some properties of twin kilohertz quasiperiodic oscillations
(QPOs) in a simple toy-model consisting of two oscillation modes coupled by a
general nonlinear force. We examine resonant effects by slowly varying the
values of the tunable, and nearly commensurable, eigenfrequencies. The behavior
of the actual oscillation frequencies and amplitudes during a slow transition
through the 3:2 resonance is examined in detail and it is shown that both are
significantly affected by the nonlinearities in the governing equations. In
particular, the amplitudes of oscillations reflect a resonant exchange of
energy between the modes, as a result the initially weaker mode may become
dominant after the transition. We note that a qualitatively similar behavior
has been recently reported in several neutron star sources by Torok (2008,
arXiv:0812.4751), who found that the difference of amplitudes in neutron star
twin peak QPOs changes sign as the observed frequency ratio of the QPOs passes
through the value 3:2.
