## 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**

**Abstract:**

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