P. G. Vaidya
Tim Doughty
Rong He
Dept. of Mech. and Mater. Eng., Washington State Univ., Pullman, WA 99164-2920
There are two unrelated developments that form the basis for research. One of these is the work by Weisenfeld [J. Stat. Phys. (1985)]. He showed that a small amount of noise would have a profound effect on the output spectrum of a nonlinear system undergoing bifurcations. These modifications thus serve as the precursors of these bifurcations. The second is the development of the trans-spectral coherence technique for the analysis of nonlinear signals, developed by Vaidya and Anderson [J. Acoust. Soc. Am. 89, 2370--2378 (1991)]. This technique has been used to educe small signals out of noise and to show inherent structure in chaos. These two ideas are put together to show that such precursors of chaos could be detected, even earlier, using the trans-spectral coherence technique. Such detection, would have a wide range of applications, from cardiology to oceanography.