Chapter 3, Exploration 18

Explore the dynamics of the system \(x_{n+1} = f_a(x) = ax_n(1-x_n)\). The dropdown menu lets you select different values for \(a\). Use the slider along the horizontal axis to change the initial condition. Determine the values of \(a\) for which the fixed point at \(x = 0\) is attracting, repelling, or neither.