Zy. Jiang et al., ANALYTIC INVESTIGATION OF CHAOS IN A CLASS OF PARABOLIC RAY SYSTEMS, The Journal of the Acoustical Society of America, 101(4), 1997, pp. 1971-1980
It has been shown that acoustic ray paths in range-dependent ocean mod
els exhibit chaotic behavior. Most of the investigations into the ray
chaos phenomenon have been primarily numerical in nature. Analytical d
erivation of sufficient conditions for chaos in acoustic systems has b
een restricted to inherently discrete problems. This article reports a
theoretical study of the existence of ray chaos in a class of continu
ous parabolic ray systems. This class of ray systems is indexed by a f
amily of analytically prescribed double-channel sound-speed profiles p
erturbed by periodic range-dependent disturbances. The perturbed Hamil
tonian ray systems are studied analytically via the Melnikov method. I
t is shown that, under certain conditions, ray trajectories of the sys
tems are equivalent to trajectories of a classic chaotic system known
as the horseshoe map when the perturbation is periodic and small. Thes
e conditions are sufficient for ray chaos and easily satisfied, thus e
xplaining why double-channel propagation is very likely to exhibit cha
otic behavior. (C) 1997 Acoustical Society of America.