A Simulation Research on Chaotic Behavior of Parabolic and Elliptic Underwater Acoustic Ray Equations

The chaotic behavior of underwater ray system is studied. Because the parabolic equation is an approximation under small ray angle with respect to horizontal, the elliptic equation system is considered here besides the parabolic system. We pay main attention to the interval of large ray angle. A comparison between these two forms of system is performed. We find that when the ray angle is not large (θ_0=0° - 18°), the two systems show the same qualitative behavior. However, in interval of large ray angle (θ_0 ≥ 19°), if the perturbation strength is not very small, e.g. δ=0.05, the parabolic system shows regular motion, while the elliptic system exhibits chaotic behavior in most of this interval except a few quasiperiodic islands studded in the chaotic ocean. Dynamical behaviors of the two systems show surprising difference.