# Attractor comparisons based on density

## Abstract

Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.

- Authors:

- US Naval Research Lab, Washington, DC 20375 (United States)

- Publication Date:

- OSTI Identifier:
- 22402525

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 1; Other Information: (c) 2015 U.S. Government; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; CHAOS THEORY; DECISION TREE ANALYSIS; DENSITY; GRAPH THEORY; LEARNING; ONE-DIMENSIONAL CALCULATIONS; PATTERN RECOGNITION; PHASE SPACE; POLYNOMIALS; SIMULATION; VECTOR FIELDS; VECTORS

### Citation Formats

```
Carroll, T. L., E-mail: Thomas.Carroll@nrl.navy.mil.
```*Attractor comparisons based on density*. United States: N. p., 2015.
Web. doi:10.1063/1.4906342.

```
Carroll, T. L., E-mail: Thomas.Carroll@nrl.navy.mil.
```*Attractor comparisons based on density*. United States. doi:10.1063/1.4906342.

```
Carroll, T. L., E-mail: Thomas.Carroll@nrl.navy.mil. Thu .
"Attractor comparisons based on density". United States.
doi:10.1063/1.4906342.
```

```
@article{osti_22402525,
```

title = {Attractor comparisons based on density},

author = {Carroll, T. L., E-mail: Thomas.Carroll@nrl.navy.mil},

abstractNote = {Recognizing a chaotic attractor can be seen as a problem in pattern recognition. Some feature vector must be extracted from the attractor and used to compare to other attractors. The field of machine learning has many methods for extracting feature vectors, including clustering methods, decision trees, support vector machines, and many others. In this work, feature vectors are created by representing the attractor as a density in phase space and creating polynomials based on this density. Density is useful in itself because it is a one dimensional function of phase space position, but representing an attractor as a density is also a way to reduce the size of a large data set before analyzing it with graph theory methods, which can be computationally intensive. The density computation in this paper is also fast to execute. In this paper, as a demonstration of the usefulness of density, the density is used directly to construct phase space polynomials for comparing attractors. Comparisons between attractors could be useful for tracking changes in an experiment when the underlying equations are too complicated for vector field modeling.},

doi = {10.1063/1.4906342},

journal = {Chaos (Woodbury, N. Y.)},

number = 1,

volume = 25,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}