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Conclusion

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 tex2html_wrap_inline803. Depending on the initial point in the phase plane tex2html_wrap_inline883 it will either reach the point with tex2html_wrap_inline935 or tex2html_wrap_inline1035. 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.


next up previous
Next: References Up: A minimal model of Previous: The waves: propagation of

Werner von Bloh (Data & Computation)
Thu Jul 13 15:02:47 MEST 2000