Response of a nonlinear Hamiltonian system to the external harmonic field: Resonant and chaotic cases

The response of a classical nonlinear oscillator to the homogeneous external field with harmonic time dependence is studied beyond the domain of applicability of the perturbation theory. The new quantity, a harmonic susceptibility (HS) that is proportional to the ensemble average of the Fourier amplitude of motion with the same frequency and phase as the external field, is introduced. In the off-resonant region, HS tends asymptotically to usual linear susceptibility. The cases of the intermediate field strength, when the isolated nonlinear resonance prevails, and that of the strong field, when the resonances overlap and the extended chaotic component is formed in the phase space, are studied. For both cases the analytical expressions for HS are obtained in the form of quadratures and confirmed by the comparison with the results of direct numerical simulation. [S1063-651X(99)06812-9].