Another phenomenon associated with chaos is what is called period doubling route to chaos. Any chaotic motion for a while would be periodic. So, for example, in this plot it shows that for values of Kp up till some amount it is nice and periodic. But after a certain period there are two possible branches, and these two branches will again break up and form many more branches. This is what is called as a period doubling route to chaos. This can also be seen in this plot where we see that it is periodic up to here, then two branches, then four branches, and then after a while too many branches are there so the whole region becomes hazy.

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