TY - JOUR
T1 - Higher-dimensional targeting
AU - Kostelich, Eric
AU - Grebogi, Celso
AU - Ott, Edward
AU - Yorke, James A.
PY - 1993
Y1 - 1993
N2 - This paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations. Such a procedure is called targeting. Previous work on targeting for chaotic attractors has been in the context of one- and two-dimensional maps. Here it is shown that targeting can also be done in higher-dimensional cases. The method is demonstrated with a mechanical system described by a four-dimensional mapping whose attractor has two positive Lyapunov exponents and a Lyapunov dimension of 2.8. The target is reached by making very small successive changes in a single control parameter. In one typical case, 35 iterates on average are required to reach a target region of diameter 10-4, as compared to roughly 1011 iterates without the use of the targeting procedure.
AB - This paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations. Such a procedure is called targeting. Previous work on targeting for chaotic attractors has been in the context of one- and two-dimensional maps. Here it is shown that targeting can also be done in higher-dimensional cases. The method is demonstrated with a mechanical system described by a four-dimensional mapping whose attractor has two positive Lyapunov exponents and a Lyapunov dimension of 2.8. The target is reached by making very small successive changes in a single control parameter. In one typical case, 35 iterates on average are required to reach a target region of diameter 10-4, as compared to roughly 1011 iterates without the use of the targeting procedure.
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U2 - 10.1103/PhysRevE.47.305
DO - 10.1103/PhysRevE.47.305
M3 - Article
AN - SCOPUS:0001673690
VL - 47
SP - 305
EP - 310
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
SN - 1539-3755
IS - 1
ER -