I plotted the variable x versus the parameter b, b is varying between 0 and 1.
   inclreasing l induces a series of period-doubling bifurcation where a stable point drive to cycles of increasing period.


here we can notice the first period-doubling bifurcation before a chaotic behaviour.

when b is lower than 0.4 we have a convergence to one point then for 0.4< b <0.59 it converge to 2 points then 4 then 8 then ... until a chaotic behavior, and we can notice in the same times that for b between 0.65 and 0.9 the system is chaotic.