Parametrization

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

1. Let
   
   and substituting C by C=A-N, we get (see Fig. 5)
    
   A good approximation for (see Fig. 6) is given by the function:
   
   Then
   
   or
   
   
2. Let
   
   where is the tolerance interval for vegetation, , i.e. the length of this interval. It is obvious that and .
3. For parametrization of f(N) we must remember that . Because can be described by parabola , and, respectively,
   
   

Using this parametrization we can investigate the evolution of the phase plane with an increase of the bifurcation parameter A.

 
• The behaviour of as a function of A
• Equilibrium as a function of and A
• The ``naked'' planet