E. Simiu et M. Grigoriu, NON-GAUSSIAN NOISE EFFECTS ON RELIABILITY OF MULTISTABLE SYSTEMS, Journal of offshore mechanics and Arctic engineering, 117(3), 1995, pp. 166-170
For certain types of compliant structures, the designer must consider
limit states associated with the onset of fluidelastic instability. Th
ese limit states may include bifurcations from motion in a safe region
of phase space to chaotic motion with exits (jumps) out of the safe r
egion. In practice, such bifurcations occur in systems with noisy or s
tochastic excitations. For a wide class of dynamical systems, a fundam
ental connection between deterministic and stochastic chaos allows the
application to stochastic systems of a necessary condition for the oc
currence of chaos originally obtained by Melnikov for the deterministi
c case, We discuss the application of this condition to obtain probabi
lities that chaotic motions with jumps cannot occur in multistable sys
tems excited by processes with tail-limited marginal distributions.