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Math Help - dynamical system

  1. #1
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    dynamical system

    hey, can anybody help?
    i have a 1 dimensional dynamical system in which x is greater than 0
    x(with a dot on top)=f(x)=1-(5x^2)+(4x^4)
    how to i solve f(x*)=0 and find its fixed points?
    thanks
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  2. #2
    Senior Member vincisonfire's Avatar
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    Reply

    You want to solve
     0 = 4\cdot x^4 - 5\cdot x^2+1
    Let  u = x^2
    Then  0 = 4\cdot u^2 - 5\cdot u+1
    And you solve the quadratic
     u = \frac {5 \pm  \sqrt{25-9}}{8}
     x = \pm\sqrt {u} = \pm 1 or \pm \frac{1}{2}
    Last edited by vincisonfire; October 19th 2008 at 10:38 AM.
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