The local analysis of singular points and their stability can not answer us the question: Do dissipative structures exist here, i.e. do other solutions, except constants, exist in this problem? In order to get the answer, we have to test them in relation to the diffusive instability (see [12, 13]).
The validity of the following inequality (at the corresponding equilibria
determined in the previous section) is a necessary and sufficient condition for the diffusive instability:
where 
; 
.
From eq. (12) we have
where 
; 
;
; 
.
If 
then from eq. (13) we get
Obviously that 
must be negative, i.e. this equilibrium is
a stable node, but in this case the inequality is not valid for all values
of 
, 
and 
.
If the equilibrium is non-trivial, i.e. 
, then
We can see in this case that the diffusive instability does not exist either.
And finally we can say that in this problem there are not the spatially non-uniform solutions (differing out of constant) like dissipative structures.