Targeting unknown and unstable periodic orbits.
We present a method to target and subsequently control (if necessary) orbits of specified period but otherwise unknown stability and position. For complex systems where the dynamics is often mixed [e.g., coexistence of regular and chaotic regions in area-preserving (Hamiltonian) systems], this targeting algorithm offers a way to not only gently bring the system from the chaotic domain to an unstable periodic orbit (where control is applied), but also to access stable regions of phase space (where control is not necessary) from within the stochastic regions. The technique is quite general and applies equally well to dissipative or conservative discrete maps and continuous flows.
Doyon
B
B
Département de Physique, de Génie Physique, et d'Optique, Université Laval, Cité Universitaire, Québec, Canada G1K 7P4.
Dubé
L J
LJ