Onset of Chaos

nAt low values of *k*
(<3), the value of *x**t* eventually stabilises to a single value - a *fixed point **attractor*nWhen *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.