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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>Phase space representation</TITLE><META NAME="description" CONTENT="Phase space representation"><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="tex2html115" HREF="node6.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html113" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html107" HREF="node4.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html116" HREF="node6.html">Delay coordinates</A><B>Up:</B> <A NAME="tex2html114" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html108" HREF="node4.html">General computational issues</A><BR> <P><H1><A NAME="SECTION00030000000000000000">Phase space representation</A></H1><A NAME="secdelay"> </A>Deterministic dynamical systems describe the time evolution of a system in somephase space <IMG WIDTH=52 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline6541" SRC="img8.gif">. They can be expressed for example byordinary differential equations<BR><A NAME="eqode"> </A><IMG WIDTH=500 HEIGHT=16 ALIGN=BOTTOM ALT="equation4408" SRC="img9.gif"><BR>or in discrete time <IMG WIDTH=55 HEIGHT=12 ALIGN=BOTTOM ALT="tex2html_wrap_inline6543" SRC="img10.gif"> by maps of the form<BR><A NAME="eqmap"> </A><IMG WIDTH=500 HEIGHT=16 ALIGN=BOTTOM ALT="equation4413" SRC="img11.gif"><BR>A time series can then be thought of as a sequence of observations<IMG WIDTH=89 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline6545" SRC="img12.gif"> performed with some measurement function <IMG WIDTH=22 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline6547" SRC="img13.gif">. Sincethe (usually scalar) sequence <IMG WIDTH=30 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline6549" SRC="img14.gif"> in itself does not properly representthe (multidimensional) phase space of the dynamical system, one has to employ sometechnique to unfold the multidimensional structure using the available data.<P><BR> <HR><UL><A NAME="CHILD_LINKS"> </A><LI> <A NAME="tex2html117" HREF="node6.html#SECTION00031000000000000000">Delay coordinates</A><LI> <A NAME="tex2html118" HREF="node7.html#SECTION00032000000000000000">Embedding parameters</A><UL><LI> <A NAME="tex2html119" HREF="node8.html#SECTION00032100000000000000">Mutual information</A><LI> <A NAME="tex2html120" HREF="node9.html#SECTION00032200000000000000">False nearest neighbors</A></UL> <LI> <A NAME="tex2html121" HREF="node10.html#SECTION00033000000000000000">Principal components</A><LI> <A NAME="tex2html122" HREF="node11.html#SECTION00034000000000000000">Poincaré sections</A><LI> <A NAME="tex2html123" HREF="node12.html#SECTION00035000000000000000">SVD filters</A></UL><HR><A NAME="tex2html115" HREF="node6.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="icons/next_motif.gif"></A> <A NAME="tex2html113" HREF="TiseanHTML.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="icons/up_motif.gif"></A> <A NAME="tex2html107" HREF="node4.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="icons/previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html116" HREF="node6.html">Delay coordinates</A><B>Up:</B> <A NAME="tex2html114" HREF="TiseanHTML.html">Practical implementation of nonlinear </A><B> Previous:</B> <A NAME="tex2html108" HREF="node4.html">General computational issues</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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