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Asymptotic behaviour

  1. Feb 8, 2007 #1
    i have the ode

    dx/dt = x^4 +4(x^3) - 60(x^2)

    generally the solution s x(t) satisfy x(0) = x[0]

    and i found out that the
    attactor is -10
    repellor is 6
    and 0 is niether

    however i want to describe the asymptotic behaviour of the solution satisfying x(0) = 1/2 , which is were i got stuck??
  2. jcsd
  3. Feb 9, 2007 #2


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    Science Advisor

    dx/dt= x^4 +4(x^3) - 60(x^2) = x^2(x^2+ 4x- 60)= x^2(x-6)(x+10).

    If x(0)= 1/2, between 0 and 6, then three of the factors, x, x, and (x+ 10) are positive while the fourth, x- 6, is negative. That means that the solution is decreasing- and, as long as it stays between 0 and 6, is always decreasing. Since the solution curve cannot cross x= 0 (because of uniqueness) this solution will go to 0 as x-> infinity.
  4. Mar 12, 2007 #3

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