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Some Nonlinear
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Vibe:Various Nonlinear Oscillators:Chaotic Oscillator

This oscillator acts as a chaotic attractor. If you watch the top window and see the position of the oscillator change over time, you'll notice that the movement seems almost random. And if you look at the bottom plot you'll notice that the oscillator doesn't return to the same position twice. Put differently, this chaotic attractor is not a limit cycle system. Yet the system is clearly not random, for there are two basins of attraction that show up in the bottom position/velocity plot. (To see these basins more clearly, select Trails.)

So why is this oscillator chaotic? In fact, the chaos of this system doesn't show up until all three variables (time, position, velocity) are exploited. If we strobe the system periodically and mark the position and velocity of the oscillator each time we strobe, we can see a pattern emerge. This pattern is fractal in nature and reveals the chaotic organization of this oscillator. By selecting Strobe and deselecting Trails you can watch the pattern emerge. However, this takes a long time, so you'll either have to be patient or try running the simulation with 1000 timesteps already completed (pending...)


Vibe Oscillator Simulator © 2000-2003 Douglas S. Eck.
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Thu Jul 24 09:12:34 EDT 2003