<?xml version="1.0" encoding="ISO-8859-1" standalone="no"?>
<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>bifish</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="bifish"> shows a bifurcation diagram in a fish population discrete time model</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>bifish([f_ch])  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>f_ch</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: can be one of <VERB>fish</VERB>, <VERB>fishr</VERB> and <VERB>fishr2</VERB>. This option selects the population model.</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    The dynamical system <VERB>fish</VERB> is the following :</P>
    <VERBATIM>
<![CDATA[
           y=b*exp(-0.1*(x(k)_1+x(k)_2));
           x(k+1)=[ y 2*y ; s 0.0]*x(k);
   ]]>
    </VERBATIM>
    <P>
    and the parameters <VERB>s</VERB> evolves to show the bifurcation diagram.
    <VERB>fishr</VERB> and <VERB>fishr2</VERB> are constructed as above but with added white noises.</P>
    <VERBATIM>
<![CDATA[
 fishr
 y=b*exp(-0.1*(xk(1)+xk(2))) 
 xkp1=[ y 2*y ; s*(1+0.1*(rand()-0.5)) 0.0]*xk

 fishr2
 z=exp(-0.1*(xk(1)+xk(2))) 
 xkp1=[ b*z**(1+0.1*(rand()-0.5)) 2*b*z**(1+0.1*(rand()-0.5)) ; s 0.0]*xk
   ]]>
    </VERBATIM>
    <P>
    The three macros <VERB>fish, fishr, fishr2</VERB> are loaded in Scilab when calling <VERB>bifish</VERB>.</P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>ode</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
