Stationary states of the map

We can easily determine the stationary-state values of x for the present map. We require simply that x +1 = x , i.e. we must solve 

One solution is x = 0. Non-zero solutions are also possible, with 

If we are to require that x (and hence xB+1) should remain in the range between zero and unity, we have the following restriction on the parameter A  

We have seen that for A = 2 the system evolves to the stationary state, i.e. we have a stable solution. How does the response change as we vary A A stationary-state solution exists across the whole range, but is it always stable  

---