nAt low values of k
(<3), the value of xteventually stabilises to a single value - a fixed point attractornWhen k is 3, the system changes to oscillate between two values. This is called a bifurcation event. Now have a limit cycle attractor of period 2.
nAs k increases, further
bifurcation events occur such that the periodicity of the attractor becomes 4, 8, 16 etc.