Turbulence and periodic oscillations are easily seen with an optically bistable device with a delay in the feedback. The device is a hybrid, having both optical and electronic components. The details of the time-dependent output are investigated. In particular, as the input intensity is increased, the device output goes through a series of second-order nonequilibrium phase transitions or bifurcations. A truncated period-doubling sequence is observed prior to the onset of turbulence or chaos. The truncation is shown to be due to a noise-induced bifurcation gap. Within the chaotic regime, the device largely follows the reverse bifurcation scheme of Lorenz. In addition, there is a small domain of frequency-locked behavior that exists within the chaotic domain. These frequency-locked waveforms represent an alternate path to chaos. With the route to choas well understood, it remained to characterize the erratic motion itself. Dimension and correlation entropy are measured for various settings of our hybrid device. The measured dimension is found to be significantly less than dimensions consistent with a conjecture due to Kaplan and Yorke. The standard method of determining correlation entropy is shown to yield more than one value.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/184440 |
| Date | January 1988 |
| Creators | Kaplan, David Louis. |
| Contributors | Hopf, Frederic A., Gibbs, Hyatt M., Shoemaker, Richard L. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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