Chaotic Dynamics and Bursting

When an adaptive algorithm is placed inside a feedback loop, the potential for instability exists. This paper demonstrates that the bursting phenomenon (first encountered by Anderson) is generic to such systems, and is not a unique feature of adaptive control. Points towards possible solutions in the hybrid case.

W. A. Sethares, C. R. Johnson, Jr., C. Rohrs, "Bursting in Adaptive Hybrids," IEEE Trans. on Communications, Vol. 37, No. 8, pp. 791-799, Aug. 1989.

Z. Ding, C. R. Johnson, Jr., and W. A. Sethares, "Frequency dependent bursting in adaptive echo cancellation and its prevention using double talk detectors," Int. Journal of Adaptive Control and Signal Processing, Vol. 4, pg. 219-236, 1990.

First demonstration that the bursting of hybrids is due to a bifurcation in the underlying adaptive system. Chaotic dynamics revealed. Argues that this is the cause of bursting in virtually all adaptive systems where the adaptive element lies inside a feedback loop.

W. A. Sethares and I. M. Y. Mareels, "Dynamics of an adaptive hybrid," IEEE Trans. on Circuits and Systems, Vol. 38, No. 1, pp. 1-11, Jan. 1991.

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