We suppose the climate of our world is determined by the temperature
T(x,t) only, and the dynamics is described by the equation
where 
is the world ``area'', A is the albedo of planet surface at a
given point x, 
is the solar constant, so that the term 
is the
insolation, and the term 
(where 
is the Stephan-Boltzmann
constant) is the erradiation. The latters can be presented in the
Budyko's form [5] also: a+bT, but it is not principally.
The Budyko form together with the empirical constants a,b would give us a better agreement with the real radiation data of the earth.
For a review of the so-called energy-balance models see, e.g., [6].
Let us
rewrite eq.(1) in the form:
Further we suppose that the planet surface can be covered by the vegetation with
the density N(x,t), its dynamics is described by a logistic equation:
where 
is the Malthusian parameter [7] of the growth function.
Now we formulate two hypotheses, which are the description of feedbacks
between the climate and vegetation of our world.
Figure 1: Albedo A as a function of vegetation density N
according to hypothesis 1. 
is the albedo of
the naked surface, 
of surface fully covered by vegetation.
Then the function 
will be the following (see Fig. 2). Obviously that
.
Figure 2: The function 
in (2).
We assume 
for any N>0.
Figure 3: The Malthusian growth function 
according to hypothesis 2.
Obviously that 
if 
, and 
if
, 
if 
.
On the ecological point of view, the describes the
ecological niche, defined as the interval of T with 
, for vegetation in the space of climatic factors.
And finally, the equations (2) and (3) together with the functions A(N) and
and the corresponding initial and boundary conditions make up the
biosphere for our world.