  We study the phenomena at the overlap of quantum chaos and nonclassical
statistics for the time-dependent model of nonlinear oscillator. It is shown in
the framework of Mandel Q-parameter and Wigner function that the statistics of
oscillatory excitation number is drastically changed in order-to chaos
transition. The essential improvement of sub-Poissonian statistics in
comparison with an analogous one for the standard model of driven anharmonic
oscillator is observed for the regular operational regime. It is shown that in
the chaotic regime the system exhibits the range of sub- and super-Poissonian
statistics which alternate one to other depending on time intervals. Unusual
dependence of the variance of oscillatory number on the external noise level
for the chaotic dynamics is observed.
