Today climatic change is a much debated topic: There is a huge amount of publications, which grow faster than exponential curve, speculations, etc. which mask (very successfully) on one simple fact: we conceive hardly ourselves how is the ``Biosphere machine'' operating? Therefore the role of simple (and simplest) models, so-called ``minimal models'' [1] can be very helpful, if they are sufficiently simple for understanding and possess a significant amount of the qualitative properties of the investigated system.
The analytical as well as the numerical analysis of such a conceptual model for description of the interaction of climate and vegetation is the aim of our paper. First attempts in this type of vegetation-climate modelling were done by Vernadsky[2] and then by Watson and Lovelock[3](``Daisyworld'' as a model of some hypothetical planet) and extended to 2-dimensional structures [4].
The paper is organized as follows: Firstly we will give a description of the vegetation-climate model, then an analysis of the uniform biosphere and of possible diffusive instabilities is presented. Finally the propagation of waves in the spatial model is analyzed in respect to the dependence on the initial conditions.