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The Approach to Stability for Delayed Feedback Control of Chaos for 1-dimensional Maps

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Edward Hellen (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: We investigate mathematically and experimentally the approach to stability using the Pyragas delayed proportional feedback control method applied to a chaotic finite difference 1-dimensional map. This method does not use unstable fixed points or require computational analysis and is therefore easy to implement experimentally. For measurements we use an analog electronic circuit realization of a finite difference quadratic return map. Comparison with predictions is facilitated by doing the linear stability analysis in terms of successive system values instead of errors from the fixed point. We find that the behavior of the approach to stability can be smooth and steady or appear erratic depending on the feedback gain.

Additional Information

Publication
arXiv:0807.2637
Language: English
Date: 2008
Keywords
stability, Pyragas, delayed proportional feedback, chaotic, finite difference, 1-dimensional map, chaos