It was shown that the proposed vegetation-climate model has a topological simple
phase plane, i.e. all trajectories end up in equilibrium points. Analysis of
the stability of the equilibria indicates an existence of two stable nodes for
a certain interval of 
. Depending on the initial point in the
phase plane 
it will either reach the point with 
or 
. These two equilibria coincide to the occurrence of vegetation in
our climate-vegetation model.
Diffusive instabilities do no exist either. Spatial perturbations of the system, however, lead to the development of propagating nonlinear waves. Their occurrence depends in a non-trivial way on the initial geometrical configuration. We can say that the spatial form of an ecosystem leads either to an extinction or a growth by developing ``travelling waves''.
In the next step the numerical simulations will be extended to spatial two-dimensional structures in order to see the evolution of spatio-temporal patterns. A second goal is the incorporation of a carbon cycle into this fairly simple model. Such an extension will allow us to have a more complex structure of the phase plane.