1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    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
    Thanks

    ..........Thankz
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Asymptotic behaviour
Loading...