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### Statistical dependency in chaos

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Lawrance, Anthony J. and Balakrishna, N.
(2008)
*Statistical dependency in chaos.*
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Volume 18
(Number 11).
pp. 3207-3219.
ISSN 0218-1274

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1142/S0218127408022366

## Abstract

This paper is concerned with the statistical dependency effects in chaotic map processes, both before and after their discretization at branch boundaries. The resulting processes are no longer chaotic but are left with realizable statistical behavior. Such processes have appeared over several years in the electronic engineering literature. Informal but extended mathematical theory that facilitates the practical calculation of autocorrelation of such statistical behavior, is developed. Both the continuous and discretized cases are treated further by using Kohda's notions of equidistribution and constant-sum to maps which are not onto. Some particularly structured chaotic map processes, and also well-known maps are examined for their statistical dependency, with the tailed shift map family from chaotic communications receiving detailed attention. Several parts of the paper form a brief review of existing theory.

Item Type: | Journal Item |
---|---|

Subjects: | Q Science > QA Mathematics Q Science |

Divisions: | Faculty of Science > Statistics |

Library of Congress Subject Headings (LCSH): | Chaotic behavior in systems -- Mathematics, Mappings (Mathematics) |

Journal or Publication Title: | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |

Publisher: | World Scientific Publishing Co. Pte. Ltd. |

ISSN: | 0218-1274 |

Official Date: | November 2008 |

Volume: | Volume 18 |

Number: | Number 11 |

Number of Pages: | 13 |

Page Range: | pp. 3207-3219 |

Identification Number: | 10.1142/S0218127408022366 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

References: | Abel, A. & Schwarz [2002] “Chaos communications — |

URI: | http://wrap.warwick.ac.uk/id/eprint/28683 |

Data sourced from Thomson Reuters' Web of Knowledge

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