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espm104-HollingII - checked the nullclines for y If y> 0...

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Lecture followup October 14, 2010 A follow-up on something from lecture today: In the Holling Type II example, with a functional response φ ( x ) for predator-prey encounters, I was surprised to see what looked like a mass action encounter term in the equation for predator change. That is, why do we have dy dt = - cy + dxy (1) instead of dy dt = - cy + d ( bx k + x ) (2) I wondered how much difference it would make in the phase plane, so I
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Unformatted text preview: checked the nullclines for y. If y > 0, then dy dt = 0 ⇒ N = ma b-m (3) So the phase plane hasn’t changed much – the second nullcline for y is still a vertical line. Not only that, but in eq. (1) we got to choose our parameter d = bk . If k = c ( b-m ) bma (4) then the second y nullcline is still x = c/d , which is a lot easier to write. 1...
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