## The limit behaviour of an autonomous fourth-order oscillating system under the action of random perturbations in the case of complex roots of the characteristic equation.(Ukrainian. English summary)Zbl 1249.60115

Summary: The asymptotic behaviour of an autonomous oscillating system determined by a differential equation of fourth order with small non-linear external perturbations of “white” noise and Poisson noise types is studied. The cases of two conjugate complex roots with negative real part and two conjugate pure imaginary complex roots of the characteristic equations are considered.

### MSC:

 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness