Phys. Rev. Lett. 76, 2254–2257 (1996)

Optimal Periodic Orbits of Chaotic Systems

Abstract

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Brian R. Hunt¹ and Edward Ott²
¹Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
²Institute for Plasma Research, Institute for Systems Research, and Departments of Electrical Engineering and of Physics, University of Maryland, College Park, Maryland 20742

Received 24 October 1995; published in the issue dated 25 March 1996

Invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor. Motivated by two different topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We present numerical evidence and analysis which indicate that the optimal average is typically achieved by a low period unstable periodic orbit embedded in the chaotic attractor.

URL:

http://link.aps.org/doi/10.1103/PhysRevLett.76.2254

DOI:

10.1103/PhysRevLett.76.2254

PACS:

05.45.+b

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Phys. Rev. Lett. 76, 2254–2257 (1996)

Optimal Periodic Orbits of Chaotic Systems

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