, Volume 1, Issue 3, pp 179-190

Controlling homoclinic orbits

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In this paper we analyze various control-theoretic aspects of a nonlinear control system possessing homoclinic or heteroclinic orbits. In particular, we show that for a certain class of nonlinear control system possessing homoclinic orbits, a control can be found such that the system exhibits arbitrarily long periods in a neighborhood of the homoclinic. We then apply these ideas to bursting phenomena in the near wall region of a turbulent boundary layer. Our analysis is based on a recently developed finite-dimensional model of this region due to Aubry, Holmes, Lumley, and Stone.

Communicated by John Lumley
The research of A.M. Bloch was partially supported by the U.S. Army Research Office through MSI at Cornell University and by NSF Grant DMS-8701576 and AFOSR Grant AFOSR-ISSA-87-0077, J.E. Marsden's research was partially supported by DOE Contract DE-ATO3-88ER-12097 and MSI at Cornell University and by AFOSR Contract No. 88-NA-321.