抛物和椭圆射线方程混沌行为研究

A study on chaotic behavior of parabolic and elliptic ray equations

目的研究水声射线系统的混沌行为。方法利用庞加莱截面、李雅普诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。结果射线角度较小时两种方程表现出相同的定性行为特征,而射线角度较大时,两种方程的混沌行为表现出显著的差异。结论对于水声射线混沌问题,在小射线角度区间,抛物方程是良好的近似,而在大射线角度范围内,椭圆方程才能正确反映实际水声射线系统性质。

Aim To study chaotic behavior of underwater ray system. Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section, Lyapunov exponent, and correlation dimension. Results When the ray angle is small, the two systems show the same qualitative behavior; however, when the ray angle is large, chaotic behaviors of the two systems show surprising differences. Conclusion In field of underwater acoustic ray chaos, the parabolic equation is an excellent approximation in interval of small ray angle, while in interval of large ray angle, the elliptic equation may describe properties of the practical underwater acoustic ray system accurately.