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<!DOCTYPE MAN SYSTEM "../../manrev.dtd">
<MAN>
  <LANGUAGE>eng</LANGUAGE>
  <TITLE>chaintest</TITLE>
  <TYPE>Scilab Function</TYPE>
  <DATE>April 1993</DATE>
  <SHORT_DESCRIPTION name="chaintest"> a three-species food chain model</SHORT_DESCRIPTION>
  <CALLING_SEQUENCE>
    <CALLING_SEQUENCE_ITEM>chaintest([f_l,b1,odem,xdim,npts])  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[xdot]=chain(t,x)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[z1]=ch_f1(u)  </CALLING_SEQUENCE_ITEM>
    <CALLING_SEQUENCE_ITEM>[z2]=ch_f2(u)  </CALLING_SEQUENCE_ITEM>
  </CALLING_SEQUENCE>
  <PARAM>
    <PARAM_INDENT>
      <PARAM_ITEM>
        <PARAM_NAME>f_l</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: the name of the macro which code the three-species food chain model (default value <VERB> chain</VERB>).</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
      <PARAM_ITEM>
        <PARAM_NAME>odem,xdim,npts</PARAM_NAME>
        <PARAM_DESCRIPTION>
          <SP>: are optional arguments. Their meaning and syntax can be found in the <VERB>portr3d</VERB>  help</SP>
        </PARAM_DESCRIPTION>
      </PARAM_ITEM>
    </PARAM_INDENT>
  </PARAM>
  <DESCRIPTION>
    <P>
    A call to the function <VERB>chaintest()</VERB> will interactively 
    display a phase portrait of  a three-species food chain model given by:</P>
    <VERBATIM>
<![CDATA[
 ff1= f1(x(1))
 ff2= f2(x(2))

 xdot1= x(1)*(1-x(1)) - ff1*x(2)
 xdot2= ff1*x(2) -  ff2*x(3) - 0.4*x(2)
 xdot3= ff2*x(3) - 0.01*x(3)
   ]]>
    </VERBATIM>
    <P>
    and</P>
    <VERBATIM>
<![CDATA[
 f1(u)=5*u/(1+b1*u)
 f2(u)z2=0.1*u/(1+2*u)
   ]]>
    </VERBATIM>
    <P>
    The default value for <VERB>b1</VERB> is 3.0.</P>
    <P>
    The Scilab macros <VERB>chain(t,x)</VERB>,<VERB>f1(u),f2(u)</VERB> code the dynamical system</P>
  </DESCRIPTION>
  <SEE_ALSO>
    <SEE_ALSO_ITEM>
      <LINK>portr3d</LINK>
    </SEE_ALSO_ITEM>
    <SEE_ALSO_ITEM>
      <LINK>ode</LINK>
    </SEE_ALSO_ITEM>
  </SEE_ALSO>
</MAN>
