In this paper the pair of coupled reaction-diffusion equations , in is considered, where , , and are parameters, , . The above system represents a model of chemical reaction , in gel reactor, where and are two chemical species, catalyzes its own reaction with and an inert product. The author first constructs two single-spot solutions and then investigates their stability and instability in terms of the parameters involved. The characteristic parameters and are defined in the following way: let be (unique) radially symmetric solution to the problem
Roughly speaking, the basic result can be described as follows: if and , then the system has two single-spot solutions; if , then there are no single-spot solutions.
In the case , linear instability of single-spot solutions can be described in terms of the parameters and .