dynamical system

math_lete · #1 $Old$ October 19th, 2008, 11:12 AM

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

vincisonfire · #2 $Old$ October 19th, 2008, 11:27 AM

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
$u = \frac {5 \pm \sqrt{25-9}}{8}$
$x = \pm\sqrt {u} = \pm 1 or \pm \frac{1}{2}$