On the other hand for a different set of parameters the same Duffing's equation can be shown to behave in a completely different way. And that difference can be seen in these two plots. This is the plot of the x variable versus time, and the same plot shown as a phase plot. Now, in the phase plot you can see that there are two possible places about which the trajectory or the orbit keeps on circling. This is a feature of all chaotic systems - it does not come back and repeat or it does not form what is called as a limit cycle.

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