Local false nearest neighbors and dynamical dimensions from observed chaotic data

Journal Article · Sat May 01 00:00:00 EDT 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.47.3057· OSTI ID:6563413

Abarbanel, H D.I. ^[1]; Kennel, M B ^[2]

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1. Institute for Nonlinear Science, Department of Physics, and Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, Mail Code 0402, La Jolla, California 92093-0402 (United States)
2. Institute for Nonlinear Science and Department of Physics, University of California, San Diego, Mail Code 0402, La Jolla, California 92093-0402 (United States)

The time delay reconstruction of the state space of a system from observed scalar data requires a time lag and an integer embedding dimension. The minimum necessary [ital global] embedding dimension [ital d][sub [ital E]] may still be larger than the actual dimension of the underlying dynamics [ital d][sub [ital L]]. The embedding theorem only guarantees that the attractor of the system is fully unfolded using [ital d][sub [ital E]] greater than 2[ital d][sub [ital A]], with [ital d][sub [ital A]] the fractal attractor dimension. Using the idea of [ital local] false nearest neighbors, we discuss methods for determining the integer-valued [ital d][sub [ital L]].

• DOE Contract Number: FG03-90ER14138
• OSTI ID: 6563413
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 47:5; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661000 -- General Physics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990301* -- Information Handling-- Data Handling-- (1992-)
DATA ACQUISITION
DATA ANALYSIS
FRACTALS
SCALARS
STOCHASTIC PROCESSES
SYSTEMS ANALYSIS
TIME DELAY