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Finding unstable periodic orbits fro...

Buhl, Michael.

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Finding unstable periodic orbits from chaotic time series.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Finding unstable periodic orbits from chaotic time series./
作者:	Buhl, Michael.
面頁冊數:	182 p.
附註:	Source: Dissertation Abstracts International, Volume: 65-06, Section: B, page: 2966.
Contained By:	Dissertation Abstracts International65-06B.
標題:	Physics, General. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3137228
ISBN:	0496844161

Finding unstable periodic orbits from chaotic time series.
Buhl, Michael.

Finding unstable periodic orbits from chaotic time series. - 182 p.

Source: Dissertation Abstracts International, Volume: 65-06, Section: B, page: 2966.

Thesis (Ph.D.)--University of California, San Diego, 2004.

Contained within a chaotic attractor is an infinite number of unstable periodic orbits (UPOs). Although these orbits have zero measure, they form a skeleton of the dynamics. However, they are difficult to find from an observed time series. In this thesis I present several methods to find UPOs from measured time series.

ISBN: 0496844161Subjects--Topical Terms:

1018488
Physics, General.

Finding unstable periodic orbits from chaotic time series.
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245 1 0 $a Finding unstable periodic orbits from chaotic time series.
300 $a 182 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-06, Section: B, page: 2966.
500 $a Chair: Henry D. Abarbanel.
502 $a Thesis (Ph.D.)--University of California, San Diego, 2004.
520 $a Contained within a chaotic attractor is an infinite number of unstable periodic orbits (UPOs). Although these orbits have zero measure, they form a skeleton of the dynamics. However, they are difficult to find from an observed time series. In this thesis I present several methods to find UPOs from measured time series.
520 $a In Chapter 2 I look at data measured from the stomatogastric system of the California spiny lobster as an example to find unstable periodic orbits. With this time series I use two methods. The first creates a local linear model of the dynamics and finds the periodic orbits of the model, and the second applies a linear transform to the model such that unstable orbits are stable. In addition, in this chapter I describe methods of filtering and embedding the chaotic time series.
520 $a In Chapter 3 I look at a more complicated model system where the dynamics are described by delay differential equations. Now the future state of the system depends on both the current state and the state a time tau earlier. This makes the phase space of the system infinite dimensional. I present a method for modeling systems such as this and finding UPOs in the infinite dimensional phase space.
520 $a In Chapters 4 and 5 I describe a new method to find UPOs using symbolic dynamics. This has many advantages over the methods described in Chapter 2; more orbits can be found using a smaller time series---even in the presence of noise. First in Chapter 4 I describe how the phase space can be partitioned so that we can use symbolic dynamics. Then in Chapter 5 I describe how the UPOs can be found from the symbolic time series. Here, I model the symbolic dynamics with a Markov chain, represented by a graph, and then the symbolic UPOs are found from the graph. These symbolic cycles can then be localized back in phase space.
590 $a School code: 0033.
650 4 $a Physics, General. $3 1018488
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710 2 0 $a University of California, San Diego. $3 1018093
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790 1 0 $a Abarbanel, Henry D., $e advisor
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791 $a Ph.D.
792 $a 2004
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