Optimal periodic orbits of chaotic systems

Journal Article · Thu Feb 29 23:00:00 EST 1996 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.76.2254· OSTI ID:284454

Hunt, B R; Ott, E ^[1]

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1. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

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. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 284454
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 13 Vol. 76; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ATTRACTORS
BIFURCATION
CHAOTIC SYSTEMS
DYNAMICS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
ORBITS
PERIODIC VARIATIONS
PERIODS