Autoregressive methods for chaos on binary sequences for the Lorenz attractor

P. Singh; D. D. Joseph

doi:10.1016/0375-9601(89)90107-2

Autoregressive methods for chaos on binary sequences for the Lorenz attractor

P. Singh
, D. D. Joseph

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences and the associated methods could also be used to estimate the system characteristics when one does not have access to all the variables involved in the underlying process; this is usually the case in an experimental study. We introduce an autocorrelation function for binary sequences, a one-step predictor and associated power spectra and a macroscopic approximation of the largest Lyapunov exponent.

Original language	English (US)
Pages (from-to)	247-253
Number of pages	7
Journal	Physics Letters A
Volume	135
Issue number	4-5
DOIs	https://doi.org/10.1016/0375-9601(89)90107-2
State	Published - Feb 27 1989
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1016/0375-9601(89)90107-2

Cite this

@article{2d20bf271bd74d4498a4a48c82eb17ef,

title = "Autoregressive methods for chaos on binary sequences for the Lorenz attractor",

abstract = "A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences and the associated methods could also be used to estimate the system characteristics when one does not have access to all the variables involved in the underlying process; this is usually the case in an experimental study. We introduce an autocorrelation function for binary sequences, a one-step predictor and associated power spectra and a macroscopic approximation of the largest Lyapunov exponent.",

author = "P. Singh and Joseph, \{D. D.\}",

note = "Funding Information: with or= 10.0, b= 8, r-28.0, were integrated numerically using the NAG library, subroutine D02BBF with different tolerance levels in the range 10 -4 to 10-1o. We looked at the projection of trajectories generated by ( 1.1 ) onto the xz-plane. The z-axis divides the xz-plane into two half-planes, called left and right half-planes. The projected trajectory makes closed loops in the left or right plane, or switches between half-planes. We define a binary sequence by assigning the number one to a loop in the right half-plane and the number minus one to a loop in the left half-plane. This binary sequence still contains some information about the original system with some information being lost in the process of defining the Research supported under grants from the US Army, Mathematics, the Department of Energy, the National Science Foundation and the Supercomputer Institute of the University of Minnesota.",

year = "1989",

month = feb,

day = "27",

doi = "10.1016/0375-9601(89)90107-2",

language = "English (US)",

volume = "135",

pages = "247--253",

journal = "Physics Letters A",

issn = "0375-9601",

publisher = "Elsevier B.V.",

number = "4-5",

}

TY - JOUR

T1 - Autoregressive methods for chaos on binary sequences for the Lorenz attractor

AU - Singh, P.

AU - Joseph, D. D.

N1 - Funding Information: with or= 10.0, b= 8, r-28.0, were integrated numerically using the NAG library, subroutine D02BBF with different tolerance levels in the range 10 -4 to 10-1o. We looked at the projection of trajectories generated by ( 1.1 ) onto the xz-plane. The z-axis divides the xz-plane into two half-planes, called left and right half-planes. The projected trajectory makes closed loops in the left or right plane, or switches between half-planes. We define a binary sequence by assigning the number one to a loop in the right half-plane and the number minus one to a loop in the left half-plane. This binary sequence still contains some information about the original system with some information being lost in the process of defining the Research supported under grants from the US Army, Mathematics, the Department of Energy, the National Science Foundation and the Supercomputer Institute of the University of Minnesota.

PY - 1989/2/27

Y1 - 1989/2/27

N2 - A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences and the associated methods could also be used to estimate the system characteristics when one does not have access to all the variables involved in the underlying process; this is usually the case in an experimental study. We introduce an autocorrelation function for binary sequences, a one-step predictor and associated power spectra and a macroscopic approximation of the largest Lyapunov exponent.

AB - A binary sequence is defined for the Lorenz attractor. This binary sequence contains some information about the original system. To extract this information we have used autoregressive methods from the theory of signal processing. The binary sequences and the associated methods could also be used to estimate the system characteristics when one does not have access to all the variables involved in the underlying process; this is usually the case in an experimental study. We introduce an autocorrelation function for binary sequences, a one-step predictor and associated power spectra and a macroscopic approximation of the largest Lyapunov exponent.

UR - https://www.scopus.com/pages/publications/38249025578

UR - https://www.scopus.com/pages/publications/38249025578#tab=citedBy

U2 - 10.1016/0375-9601(89)90107-2

DO - 10.1016/0375-9601(89)90107-2

M3 - Article

AN - SCOPUS:38249025578

SN - 0375-9601

VL - 135

SP - 247

EP - 253

JO - Physics Letters A

JF - Physics Letters A

IS - 4-5

ER -

Autoregressive methods for chaos on binary sequences for the Lorenz attractor

Abstract

All Science Journal Classification (ASJC) codes

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