Attracting and repelling fixed points and cycles

Question

Consider the iteration which produces the Mandelbrot set: $f(z) = z^2+c$.

• At $c=0$, this iteration has an attractive fixed point.
• At $c=-1$, it has an attractive 2-cycle.
• As $c$ varies from $0$ to $-1$, the repelling 2-cycle combines with the attractive fixed point, then splits and becomes attractive while the fixed point becomes repelling.

Questions:

1. Why does it happen in this way?
2. Why can we not have both be attracting?
3. Do the point and cycle have to combine for the change to occur?

I am specifically looking for answers that can explain the similar switch to an $n$-cycle that occurs at other bulbs of the Mandelbrot set.