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.
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- Controlling homoclinic orbits
Theoretical and Computational Fluid Dynamics
Volume 1, Issue 3 , pp 179-190
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- 1. MSI, Cornell University, 14853, Ithaca, NY, USA
- 2. Department of Mathematics, Ohio State University, 43210, Columbus, OH, USA
- 3. Department of Mathematics, University of California, 94720, Berkeley, CA, USA
- 4. Cornell University, 14853-7901, Ithaca, NY, USA