Vol.2, No 10, 2000 pp. 1137-1148
UDC 519.218.7:531.36:629.7.058.6
ASYMPTOMATIC
BEHAVIOR OF NON-LINEAR
DYNAMIC SYSTEMS
SUBJECTED TO PARAMETRIC
AND RANDOM EXCITATIONS
Svetlana Janković, Miljana Jovanović
Faculty of science, Department of Mathematics,
University of Niš
Ćirila i Metodija 2, 18000 Niš, Yugoslavia
E-mail: svjank@archimed.filfak.ni.ac.yu
mima@archimed.filfak.ni.ac.yu
Abstract. In this paper we investigate
the asymptotic behavior, in the (2k)-th moment sense, of the non-linear
oscillator amplitude subjected to small parametric perturbations and random
excitations of a Gaussian white noise type. Since this problem is essentially
connected with the stochastic differential equation of the Itô type, the
present paper deals with the asymptotic behavior of the solution of the
Itô's differential equation with small perturbations, by comparing it with
the solution of the corresponding unperturbed equation. Precisely, we give
conditions under which these solutions are close in the (2k)-th moment
sense on intervals whose length tends to infinity as small perturbations
tend to zero.
ASIMPTOTSKO
PONAŠANJE
NELINEARNIH DINAMIČKIH
SISTEMA
POD UTICAJEM
PARAMETARSKIH I SLUČAJNIH POBUDA
U radu se ispituje asimptotsko ponašanje,
u smislu momenata (2k)-tog reda, amplitude nelinearnog oscilatora pod uticajem
malih parametarskih perturbacija i slučajnih pobuda tipa Gaussovog šuma.
Pošto je ovaj problem esencijalno povezan sa stohastičkom diferencijalnom
jednačinom tipa Itôa, ovaj rad razmatra asimptotsko ponašanje rešenja Itôove
diferencijalne jednačine sa malim perturbacijama, upoređujući ga sa rešenjima
odgovarajuće neperturbovane jednačine. Preciznije, dati su uslovi pri kojima
su ova rešenja bliska u smislu momenata (2k)-tog reda na intervalima čija
dužina teži beskonačnosti kada male perturbacije teže ka nuli.
