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Fixed Points of ODE

  1. Jul 21, 2009 #1
    In a book on synchronization it is stated that given the ODE

    [tex]\frac{d\psi}{dt}=-\nu+\epsilon q(\psi)[/tex]

    there is at least one pair of fixed points if

    [tex]\epsilon q_{min}<\nu<\epsilon q_{max}[/tex]

    were [tex]q_{min}, q_{max}[/tex] are the min and max values of [tex]q(\psi)[/tex] respectively.

    While this could be true under particular circumstances (ie. when [tex]q_{min}<0, q_{max}>0[/tex]), I dont see how it could hold in general; such as the case when [tex]q(\psi)>0[/tex].

    Can anyone shed some light on this?

    Thanks in advance.
     
  2. jcsd
  3. Jul 21, 2009 #2
    Just think about this...

    [tex]
    0 = -\nu+\epsilon q(\psi)
    [/tex]
     
  4. Jul 21, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Assuming that q is continuous, the "intermediate value property" gives the answer.
     
  5. Jul 21, 2009 #4
    Yes, of course! Thank you both.
     
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