Controlling homoclinic orbits

Bloch, A. M. and J. E.¬†Marsden

Theoretical and Computational Fluid Mechanics, 1, 179-190


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 systems possessing homoclinic orbits, a control can be founds such that the system exhibits arbitrarily long periods in a neighborhood of the homoclinic orbit. We 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.