Theoretical and Computational Fluid Dynamics

, Volume 1, Issue 3, pp 179-190

First online:

Controlling homoclinic orbits

  • A. M. BlochAffiliated withMSI, Cornell UniversityDepartment of Mathematics, Ohio State University
  • , J. E. MarsdenAffiliated withDepartment of Mathematics, University of CaliforniaCornell University

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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.