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← Nonlinear 1.1 Introduction to nonlinear dynamics

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Showing Revision 4 created 07/20/2016 by Steven Gunawan.

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    Hi this is Liz Bradley, I'm a Professor
    in the Computer Science department
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    in the University of Colorado at Boulder
    and also on the external faculty of the
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    Santa Fe Institute. My research interests
    are on nonlinear dynamics and chaos and
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    in artificial intelligence, and I'm going
    to be your guide in this course on
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    nonlinear dynamics and chaos. Here's an
    example of a nonlinear dynamical system.
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    It's a double pendulum. Two pieces of
    aluminium and four ball bearings. Even
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    though the system is very simple, it's
    behavior is very complicated.
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    Moreover, this system is sensitively
    dependent on dynamical systems. If I
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    started here, or here, the future evolution
    of the behavior will be very different.
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    Even though the behavior of that device is
    very very complicated, there are some very
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    strong patterns in that behavior, and the
    tandem of those patterns and the sensitivity
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    is the hallmark of chaos. Now there's
    lots of words on this slide that we'll get
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    into over the next ten weeks. I'll just
    give you some highlights here.
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    A deterministic system is one that is not
    random. Cause and effect are linked and
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    the current state determines the future
    state.
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    A dynamic system (or a dynamical system),
    either are fine, is a system that evolves with time
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    A nonlinear system is one where the
    relationships between the variables that
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    matter are not linear. An example of a non
    linear system is the gas gauge in a car,
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    at least in my car, where I fill up the
    tank, and then I drive a hundred miles and
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    the needle barely moves. And then I drive
    another hundred miles and the needle.
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    plummets. That's a nonlinear relationship
    between the level of gas in the tank
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    and the position of the needle. Now non
    linear dynamics and chaos are not rare.
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    Of all the systems in the universe that
    evolves with time, that's the outer
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    ellipse in this Venn diagram, the vast
    majority of them are nonlinear.
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    Indeed a famous mathematician refers to
    the study of nonlinear dynamics