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    Has anyone studied and understand the transition to Chaos?

    Dynamical systems are wonderful and I am able to graphically analyse Orbits. It's just getting my head round dynamics of the quadratic map and bifurcations in general that has stumped me.

    I am expecting a bump thread here...


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    Anyone?
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    google Aaron Burton and Newton`s method. Also, if you can check out this book (i`m looking it over right now!): (2nd hand would be cheaper!)

    http://www.amazon.co.uk/First-Course.../dp/0201554062

    - has good explanation of orbits and graphical analysis of them, bifurcations, the madelbrot set (z=z^2+c), and other really cool stuff.

    the thing about bifurcations is everything can get so complicated if you don`t take it at a reasonable pace - and the above book does just that.
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    (Original post by Hasufel)
    google Aaron Burton and Newton`s method. Also, if you can check out this book (i`m looking it over right now!): (2nd hand would be cheaper!)

    http://www.amazon.co.uk/First-Course.../dp/0201554062

    - has good explanation of orbits and graphical analysis of them, bifurcations, the madelbrot set (z=z^2+c), and other really cool stuff.

    the thing about bifurcations is everything can get so complicated if you don`t take it at a reasonable pace - and the above book does just that.
    Thanks dude.. shall look into buying one, since I'm thinking of doing my MSci project in Dynamical systems (crazy I know )

    This indian guy is pretty awesome:
    Spoiler:
    Show



    I kind of have grasped bifurcation theory, it's the loss of stability right? When an attracting period-n cycle becomes reppeling and then separates and becomes an attracting n cycle again ......, (imagining the pitchfork and after a few branches it goes crazy, I'm assuming that's the Chaos part... )

    Really nervous, I still have to cover -meaning teach myself: Chaos, Chaos and Probability AND Fractals (2D Maps, Fractals and figure)

    Wish me luck... feel like a nervous breakdown is coming soon even though this module is AMAZING and cant understand how some folk can graduate with a Pure/Maths degree and not have to do this sort of analysis.

    Edit: the book is available in my library, might just pop out and get it. :awesome:
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    Name:  ImageUploadedByStudent Room1364859249.045599.jpg
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Size:  19.9 KB turns out I already have the book at home


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    (Original post by Khodu)
    ...
    I've not read too much of it, but this covers a lot of the basics like linear/planar maps and non-linear planar maps, stability, simple/flip bifurications, period doubling and so on: http://www.amazon.com/Essential-Math.../dp/185233536X

    I guess it'd go on the look at chaos etc. I've only looked at the basics as I've only done a short course in dynamical systems so far.
 
 
 
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