2pSPb1. Analysis of induced chaos in Duffing's equation, using Caseygrams.

Session: Tuesday Afternoon, May 14

Time: 2:15

Author: P. G. Vaidya
Author: C. R. Winkel
Location: School of Mech. and Material Eng., Washington State Univ., Pullman, WA 99164


In speech signals, a newer type of chaos has been observed. It could be termed as an ``induced chaos.'' In order to see if this type of chaos can be stimulated, in a theoretical setting, the Duffing's equation has been looked at. The parameters of this equation have been chosen in such a way that this would result in an output which is normally nonchaotic. However, the driving amplitude has been modulated, and in turn, the phase and the driving frequency. All of these led to ``induced chaos.'' This chaos differs in certain important characteristics from the usual chaos. It was found that the best way to detect such a chaos was to use the differential trans-spectrograms, or the ``Caseygrams.'' These are obtained by calculating the difference between two specific types of trans-spectral coherences, (TSC's) [P. G. Vaidya and M. J. Anderson, J. Acoust. Soc. Am. 89, 2370--2378 (1991)]. These two TSC's are specifically developed to measure the interaction of the main harmonics with the subharmonics. These results show that as the modulations increased the induced chaos became more and more apparent in terms of the difference between the TSC's, and thus in the Caseygram. A theoretical explanation of these results is included.

from ASA 131st Meeting, Indianapolis, May 1996