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Parametrization

In order to make our investigation simpler and more visual, we use parametric presentations for functions tex2html_wrap_inline1409, tex2html_wrap_inline1519, and f(N).

  1. Let
    equation312
    and substituting C by C=A-N, we get (see Fig. 5)
     equation317
    A good approximation for tex2html_wrap_inline1409 (see Fig. 6) is given by the function:
    equation323
    Then
    equation329
    or
    equation335
  2. Let
    equation343
    where tex2html_wrap_inline1529 is the tolerance interval for vegetation, tex2html_wrap_inline1531, i.e. the length of this interval. It is obvious that tex2html_wrap_inline1533 and tex2html_wrap_inline1535.
  3. For parametrization of f(N) we must remember that tex2html_wrap_inline1539. Because tex2html_wrap_inline1395 can be described by parabola tex2html_wrap_inline1543, and, respectively,
    equation356
Using this parametrization we can investigate the evolution of the phase plane with an increase of the bifurcation parameter A.




next up previous
Next: The behaviour of as Up: Climatevegetation, and global Previous: Stability analysis

Werner von Bloh (Data & Computation)
Thu Jul 13 11:24:58 MEST 2000