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← Nonlinear 2.3 Exploring the bifurcation diagram

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Showing Revision 1 created 12/16/2016 by Miharu Jay Kimwell.

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    In the last segment, I showed you how
    return maps work,
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    how to go back and forth between
    them and the time domain,
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    and how they help you understand the
    dynamics, as well as
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    how to understand bifurcations in the
    dynamics as the parameter value changes.
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    I finished up with a 3rd representation,
    the bifurcation diagram.
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    Here's a bifurcation diagram of
    the logistic map.
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    On the vertical axis is a set of iterates
    of the logistic map,
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    at some parameter value R, which is
    graphed on the horizontal axis.
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    Just to remind you of the correspondence
    between this kind of plot
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    and the time domain, and the return map,
    I'm gonna draw a few pictures.