AN ANALYSIS OF THE TRANS-SPECTRAL-COHERENCE FOR DUFFING OSCILLATORS UNDERGOING CHAOS

A theoretical explanation of the observed Trans-Spectral-Coherence for the signal generated from the Duffing oscillators during chaos has be en presented. As expected based on findings from earlier work by M. D. Miller strong coherence was found when the Duffing oscillators gave r ise to periodic solutions. When the solution was chaotic, it was expec ted that there would not be phase coherence at all. This was true for the phase coherence between the fundamental frequency omega and sub-ha rmonics and the fundamental frequency and even harmonics. However, for the odd harmonics, strong phase coherence between omega and 3 omega, 5 omega, etc. has been found. In order to explain this phenomenon, clo sed orbits in chaos have been theoretically analysed. These orbits hav e been subdivided into many groups. Within each group there is pi phas e shift which affects the coherence between omega and 2 omega frequenc ies and does not affect the coherence between omega and 3 omega freque ncies. This closed orbit analysis has been used to explain the numeric al results mentioned above. Similar analysis has been carried out to e xplain why the phase coherence between omega and the sub-harmonics van ishes during chaos. (C) 1998 Academic Press Limited.