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Van Der Pol system

  1. Dec 5, 2011 #1
    Hello All,

    I am struggling to understand the following passage (all eqautions can be found in a much better format at http://www.scholarpedia.org/article/Van_der_Pol_oscillator, eq(8) especially).

    Starting from (C being a constant)

    u' = C * u [4 - (u^2*v^2)]
    v' = C * v [4 - (u^2*v^2)]

    introducing

    r^2 = u^2 * v^2

    the equation

    r' = C * r [4 - (u^2*v^2)]

    I observe that squaring each equation above and summing one obtains

    (u')^2 = C^2 * u^2 [4 - (u^2*v^2)^2]
    (v')^2 = C^2 * v^2 [4 - (u^2*v^2)^2]

    Summing top and below

    (u')^2 + (v')^2 = C^2 * [4-(u^2*v^2)^2] * [u^2 + v^2]

    Is this not a contradiction with the eqaution in bold i would like to understand? I am sure of course I made a trivial mistake somewhere. Thank you for any help

    Muzialis
     
  2. jcsd
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