vdp - 2 2 4 Van der Pol oscillator: e = 0.1 x K 4 K 3 K 2 K...

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The Van der Pol oscillator The Van der Pol oscillator is governed by the second order equation x ′′ ǫ (1 x 2 ) x + x = 0 . To convert this to a system of Frst order equations in two unknowns we let y = x and Fnd x = y, y = x + ǫ (1 = x 2 ) y. What follows are phase plane plots of this system for ǫ = 0 . 1 , 0 . 5 , 1 . 0 , 1 , 5 , and 5 . 0 . Poblem 6 of Section 7.5 in Greenberg has an interesting analysis of this sytem for large ǫ .
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x K 4 K 3 K 2 K 1 0 1 2 3 4 y K 4 K
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Unformatted text preview: 2 2 4 Van der Pol oscillator: e = 0.1 x K 4 K 3 K 2 K 1 1 2 3 4 y K 4 K 2 2 4 Van der Pol oscillator: e = 0.5 x K 4 K 3 K 2 K 1 1 2 3 4 y K 4 K 2 2 4 Van der Pol oscillator: e = 1.0 x K 4 K 3 K 2 K 1 1 2 3 4 y K 4 K 2 2 4 Van der Pol oscillator: e = 1.5 x K 4 K 3 K 2 K 1 1 2 3 4 y K 10 K 5 5 10 Van der Pol oscillator: e = 5...
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vdp - 2 2 4 Van der Pol oscillator: e = 0.1 x K 4 K 3 K 2 K...

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