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Nonlinear systems of differential equations

  1. Dec 3, 2011 #1
    The complete question I've been given:
    The Rossler equations are formally defined as
    dx/dt=−y−z
    dy/dt=x+ay
    dz/dt=b+z(x−c).
    Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400].
    Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the initial value problem with x(0)=0.001, y(0)=z(0)=0. Please find (analytically an estimate of the value of tmax>0 such that |v1(t)-v2(t)|<=1 for all t∈[0,tmax]. You may assume that max{|x(t)|,|y(t)|,|z(t)|}<=25 for all t.

    Do I need to actually solve the equations and if so how?
    If i don't then what do I need to do? would approximating the system by a linear one be in the right direction?

    I've tried literally everything i can think of to solve the equations (I'm not going to put it all down here but suffice to say i got nowhere). But i'm not actually sure i should be solving them at all. If i estimate as a linear system I'm fairly sure I could solve it, that's not the problem, it's whether or not that would give me the answer i need.
     
  2. jcsd
  3. Dec 4, 2011 #2
    Ok, this is what I'd do. You mentioned linearizing it right? Yeah well I'm not sure about that. So first, just solve it numerically to get the answer. Then linearize it and compute the answer and then compare the numerically computed answer to the linearized answer.
     
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