Abstract
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.
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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.
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Bloch, A.M., Marsden, J.E. Controlling homoclinic orbits. Theoret. Comput. Fluid Dynamics 1, 179–190 (1989). https://doi.org/10.1007/BF00417919
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DOI: https://doi.org/10.1007/BF00417919