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unpredictable, not random behavior
-built upon nonlinearity and feedback
-small input=Huge output |
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o When a measurement is made there will be some amount of error involved.
In some cases observed processes are too complex to measure in detail. (ex. Statistical mechanics for behavior of gases and probability theory for prediction of events). |
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o Physics problems up until now have been stationsary and exists in time but don’t change their patterns continuously. Time has been talked about as moslt y a human perceptions.
o However, many processes around us are actively changing in time (when this occurs a critical issue is PREDICTABILITY) |
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| o Tiny errors in one system component will translate linearly into tiny errors in later system measurements. |
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| nonlinearity leads to _____ and more complicated than ________ |
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| more complicated than y = mx + b and leads to feedback |
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| if a process goes in one direction, non linear feedback makes it go that way even faster/further |
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| if a process goes in one direction, nonlinear feedback tries to make it go the other way. |
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| nonlinearity + feedback = |
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| when you get BIG changes in output when you make small changes in input. (small inBIG out) (LORENTZ) |
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| Attractors and strange attractors |
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- stable/periodic states of system – “limit cycles
-never cross/infinite line in a finite volume |
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| closed trajectory in phase space having the property that @ least one other trajectory spirals into it as time approaches infinity. (periodic orbit of isolated system) ex. swings of pendulum clock |
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| a geometric representation of the trajectroies of a dynamical system in the phase plane. Each set of initial |
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| : the range over which a real object show fractal behavior |
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