The equilibrium of the system is determined by the solution of eq. (14).
For we have
where . It is obvious that .
Since N>0 then
i.e. only within the interval , where
.
It is interesting that the interval is reduced to a point, i.e. ,
if , where is defined as
It is obvious that, if , does
not exist, and there are the solutions and alone. In Fig. 8
the different N(T), corresponding to different values of A, are shown.
The maximum of N in respect to T is . It
is obvious that and it reaches that point at
.
Figure 8: The carbon mass in vegetation in equilibrium N as a function
of the equilibrium temperature T and the total amount of carbon A in the
system. For equilibrium with N=0 exist alone.
Let us remember the stability condition for the equilibrium
(see formulas (19)-(20)).
Since ,
then from (19) it follows:
i.e. this equilibrium is stable, and if
it is unstable.
Let us compare these expressions to (36). Hence, this equilibrium is always unstable, if , and it is stable if . It is obvious that for the unique equilibrium exists and is stable.