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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.2//EN"><!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>Introduction</TITLE><META NAME="description" CONTENT="Introduction"><META NAME="keywords" CONTENT="TiseanHTML"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="TiseanHTML.css"></HEAD><BODY bgcolor=ffffff LANG="EN" > <A NAME="tex2html85" HREF="node3.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html83" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html77" HREF="node1.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html86" HREF="node3.html">Philosophy of the TISEAN </A><B>Up:</B> <A NAME="tex2html84" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html78" HREF="node1.html">Lead Paragraph</A><BR> <P><H1><A NAME="SECTION00020000000000000000">Introduction</A></H1><P>Deterministic chaos as a fundamental concept is by now well established anddescribed in a rich literature. The mere fact that simple deterministic systemsgenerically exhibit complicated temporal behavior in the presence ofnonlinearity has influenced thinking and intuition in many fields. However, ithas been questioned whether the relevance of chaos for the understanding of thetime evolving world goes beyond that of a purely philosophical paradigm.Accordingly, major research efforts are dedicated to two related questions.The first question is if chaos theory can be used to gain a betterunderstanding and interpretation of observed complex dynamical behavior. Thesecond is if chaos theory can give an advantage in predicting or controllingsuch time evolution. Time evolution as a system property can be measured byrecording time series. Thus, nonlinear time series methods will be the key tothe answers of the above questions. This paper is intended to encourage theexplorative use of such methods by a section of the scientific community whichis not limited to chaos theorists. A range of algorithms has been madeavailable in the form of computer programs by the TISEANproject [<A HREF="citation.html#tisean">1</A>]. Since this is fairly new territory, unguided use of thealgorithms bears considerable risk of wrong interpretation and unintelligibleor spurious results. In the present paper, the essential ideas behind thealgorithms are summarized and pointers to the existing literature are given.To avoid excessive redundancy with the text book [<A HREF="citation.html#KantzSchreiber">2</A>] and therecent review [<A HREF="citation.html#habil">3</A>], the derivation of the methods will be kept to aminimum. On the other hand, the choices that have been made in theimplementation of the programs are discussed more thoroughly, even if this mayseem quite technical at times. We will also point to possible alternatives tothe TISEAN implementation.<P>Let us at this point mention a number of general references on the subject ofnonlinear dynamics. At an introductory level, the book by Kaplan andGlass [<A HREF="citation.html#KaplanGlass">4</A>] is aimed at an interdisciplinary audience and providesa good intuitive understanding of the fundamentals of dynamics. Thetheoretical framework is thoroughly described by Ott [<A HREF="citation.html#Ott">5</A>], but also inthe older books by Bergé et al. [<A HREF="citation.html#Berge">6</A>] and bySchuster [<A HREF="citation.html#Schuster">7</A>]. More advanced material is contained in the work byKatok and Hasselblatt [<A HREF="citation.html#KatokHasselblatt">8</A>]. A collection of researcharticles compiled by Ott et al. [<A HREF="citation.html#coping">9</A>] covers some of the more appliedaspects of chaos, like synchronization, control, and time series analysis.<P>Nonlinear time series analysis based on this theoretical paradigm is describedin two recent monographs, one by Abarbanel [<A HREF="citation.html#abarbook">10</A>] and one by Kantz andSchreiber [<A HREF="citation.html#KantzSchreiber">2</A>]. While the former volume usually <EM>assumes</EM>chaoticity, the latter book puts some emphasis on practical applications totime series that are not manifestly found, nor simply assumed to be,deterministic chaotic. This is the rationale we will also adopt in the presentpaper. A number of older articles can be seen as reviews, including Grassbergeret al. [<A HREF="citation.html#gss">11</A>], Abarbanel et al. [<A HREF="citation.html#abarbanel">12</A>], as well as Kugiumtzis etal. [<A HREF="citation.html#kugiumtzis_rev1">13</A>, <A HREF="citation.html#kugiumtzis_rev2">14</A>]. The application of nonlinear timeseries analysis to real world measurements where determinism is unlikely to bepresent in a stronger sense, is reviewed in Schreiber [<A HREF="citation.html#habil">3</A>]. Apart fromthese works, a number of conference proceedings volumes are devoted to chaotictime series, including Refs. [<A HREF="citation.html#Mayer-Kress">15</A>, <A HREF="citation.html#casdagli">16</A>, <A HREF="citation.html#SFI">17</A>, <A HREF="citation.html#dyndis">18</A>, <A HREF="citation.html#freital">19</A>].<P><BR> <HR><UL><A NAME="CHILD_LINKS"> </A><LI> <A NAME="tex2html87" HREF="node3.html#SECTION00021000000000000000">Philosophy of the TISEAN implementation</A><LI> <A NAME="tex2html88" HREF="node4.html#SECTION00022000000000000000">General computational issues</A></UL><HR><A NAME="tex2html85" HREF="node3.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html83" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html77" HREF="node1.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html86" HREF="node3.html">Philosophy of the TISEAN </A><B>Up:</B> <A NAME="tex2html84" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html78" HREF="node1.html">Lead Paragraph</A><P><ADDRESS><I>Thomas Schreiber <BR>Wed Jan 6 15:38:27 CET 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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