  A chaotic autonomous Hamiltonian systems, perturbed by small damping and
small external force, harmonically dependent on time, can acquire a strange
attractor with properties similar to that of the canonical distribution - the
Gibbs attractor. The evolution of the energy in such systems can be described
as the energy diffusion. For the nonlinear Pullen - Edmonds oscillator with two
degrees of freedom the properties of the Gibbs attractor and their dependence
on parameters of the perturbation are studied both analytically and
numerically.
