Theoretical and Computational Fluid Dynamics

, Volume 1, Issue 3, pp 179–190

Controlling homoclinic orbits

  • A. M. Bloch
  • J. E. Marsden

DOI: 10.1007/BF00417919

Cite this article as:
Bloch, A.M. & Marsden, J.E. Theoret. Comput. Fluid Dynamics (1989) 1: 179. doi:10.1007/BF00417919


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.

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • A. M. Bloch
    • 1
    • 2
  • J. E. Marsden
    • 3
    • 4
  1. 1.MSI, Cornell UniversityIthacaUSA
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  4. 4.Cornell UniversityIthacaUSA