PL EN


Preferences help
enabled [disable] Abstract
Number of results
2013 | 123 | 1 | 53-57
Article title

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

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
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.
Keywords
EN
Publisher

Year
Volume
123
Issue
1
Pages
53-57
Physical description
Dates
published
2013-01
received
2012-02-21
(unknown)
2012-10-23
Contributors
author
  • School of Computer Science & Technology, Xi'an University of Posts & Telecommunications, Xi'an 710121, China
author
  • Institute of Photonics and Photon-Technology, Northwest University, Xi'an 710069, China
References
  • [1] D.R. Palmer, M.G. Brown, F.D. Tappert, H.F. Bezdek, Geophys. Res. Lett. 15, 569 (1988)
  • [2] T. Bódai, A.J. Fenwick, M. Wiercigroch, J. Sound Vibrat. 324, 850 (2009)
  • [3] T. Bódai, A.J. Fenwick, M. Wiercigroch, Int. J. Bifurcat. Chaos 18, 1579 (2008)
  • [4] I.P. Smirnov, A.L. Virovlyansky, G.M. Zaslavsky, J. Acoust. Soc. Am. 117, 1595 (2005)
  • [5] T. Bódai, A.J. Fenwick, M. Wiercigroch, Int. J. Bifurcat. Chaos 19, 2953 (2009)
  • [6] K.B. Smith, M.G. Brown, F.D. Tappert, J. Acoust. Soc. Am. 91, 1939 (1992)
  • [7] X.J. Li, Y. Zhang, G.H. Du, J. Acoust. Soc. Am. 105, 2142 (1999)
  • [8] X.J. Li, G.H. Du, J. Opt. Soc. Am. B 18, 318 (2001)
  • [9] Y.A. Li, X.J. Li, J.T. Bai, J. Northwest Univ. (Natural Science Edition) 34, 165 (2004) (in Chinese)
  • [10] M. Eissa, M. Kamel, H.S. Bauomy, Int. J. Bifurcat. Chaos 21, 195 (2011)
  • [11] F.D. Tappert, in: Physics, Vol. 70, Wave Propagation and Underwater Acoustics, Eds. J.B. Keller, J.S. Papadakis, Springer-Verlag, New York 1977, p. 224
  • [12] K.B. Smith, M.G. Brown, F.D. Tappert, J. Acoust. Soc. Am. 91, 1950 (1992)
  • [13] W.H. Munk, J. Acoust. Soc. Am. 55, 220 (1974)
  • [14] J. Yan, J. Acoust. Soc. Am. 94, 2739 (1993)
  • [15] P. Grassberger, I. Procaccia, Physica D 9, 189 (1983)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv123n112kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.