<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>recur</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="recur"> a bilinear recurrent equation</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>[y]=recur(x0,var,k,n)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[integr]=logr(k,var)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <DESCRIPTION>
    <P>
    computes solutions of a bilinear recurrent equation</P>
    <VERBATIM>
<![CDATA[
x(i+1)=-x(i)*(k + sqrt(var)*br(i))
   ]]>
    </VERBATIM>
    <P>
    with initial value <VERB>x0</VERB> and driven by a white noise 
    of variance <VERB>var</VERB>.</P>
    <P>
    Trajectories are drawn and the empirical Lyapunov exponent 
    is returned 
    ( <VERB>x(i)</VERB> is not to much different from <VERB>exp(y*i)</VERB> )</P>
    <P>
    A theoretical computation of the Lyapunov exponent 
    is given by</P>
    <VERBATIM>
<![CDATA[
[integr]=logr(k,var)
   ]]>
    </VERBATIM>
  </DESCRIPTION>
</MAN>
