Chaos vs. Order: Is there a Transition Zone?

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Is there a line between a system in chaos and one not in chaos? Alternatively, is there a transition zone? If such things do exits, what are they called?
 

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You are really talking about the boundary of basins of attraction. And a basin of attraction can be "periodic", "quasi-periodic", or "chaotic" so your "transition zone between chaos and non-chaos" is a boundary between a chaotic basin of attraction and a basin of atraction that is not chaotic.
 

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