Given the following 1D map, $p_{n+1} = (1-\lambda) \cdot p_{n} + \lambda \cdot \frac{a}{b} - \lambda \cdot \frac{\arctan(\mu \cdot p_{n})}{b}$
The fix point is found by,
$p_{n+1} = p \implies (1-\lambda) \cdot p_{n} + \lambda \cdot \frac{a}{b} - \lambda \cdot \frac{\arctan(\mu \cdot p_{n})}{b} = p \implies p + \arctan(\mu \cdot p) = a$
Trying to solve this analytically where I fix the values for every parameter beside a, but Maple has problems with giving an expression for p. Would like to denote by use of intervals for $a$ where the map is stable, unstable and so on.
Is there any way this fix point can be found analytically ?