Abstract.Here we purpose a simple but realistic model of one dimensional nonlinear Kapitza oscillator driven by sin-or cos-rapidly external oscillating periodical force. The model has a parameter 2gl/a 2 γ 2 of dimension one, depending on the amplitude a and frequency of modulation γ. Changing its value we construct phase portraits of the system in the neighbourhood of fixed points and demonstrate the changing in Lyapunov spectrum. Our purpose is to observe the behavior of system at fixed points due to the different structures of the Lyapunov spectra.Key words and Phrases: Kapitza oscillator, Lyapunov spectrum, Lyapunov spectra. Abstrak. Pada paper ini disajikan sebuah model sederhana tapi realistis dariosilator Kapitza nonlinear dimensi satu yang dikendalikan oleh gaya luar berosilasi periodik sin-dan cos-dengan cepat. Model ini mempunyai parameter 2gl/a 2 γ 2 satu dimensi, bergantung pada amplitudo a dan frekuensi modulasi γ. Dengan merubah nilai parameternya, kami mengkonstruksi diagram fasa dari sistim pada ketetanggaan titik tetap dan mendemonstrasikan perubahan spektrum Lyapunov.Kemudian, kami menyajikan pengamatan dari tingkah laku sistim pada titik tetap dikaitkan dengan struktur dari spektral Lyapunov.

We propose open-loop control model of focusing cooled quantum particles in 1D and 2D modulated optical field. Applying Kapitza's procedure of averaging, we demonstrate that the type of attractor in the fixed points can be controlled by changing the parameters of control optical field. We support our conclusions by simulation for harmonic control.