Modeling interactions 2

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Modeling interactions 2
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Lotka Volterra model of prey predator
interaction
H prey density, P predator density
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Equilibria
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Phase portrait - nullclines
P
H
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Time domain solutions
H
P
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Do hares eat lynx ? M.Gilpin, Am. Naturalist,
1973
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State trajectories follow closed cycles

• Can we use linearization argument to prove it ?
• First integral

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What happens when prey compete ?
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Phase portrait
P
H
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H
P
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Diff. equations with squared variables on the
right hand side can show finite escape times