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predprey

# predprey - each case you should see that the predator lags...

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The Predator-Prey System (Lotka-Volterra equations) If x is the prey species and y the predator, then the Lotka-Volterra equations are x = x ( a αy ) , y = y ( c + γx ) where a, c, α , and γ are positive constants. For the graphs that follow we take a = 1 . 4, c = 2 . 0, α = 0 . 8, and γ = 1 . 2. We plot the phase plane, followed by solution curves for two different initial conditions. It is a good exercise to trace a solution around a trajectory in the phase plane, noticing when x and y increase and decrease, and to compare the result with the soltuion curves.

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Unformatted text preview: each case you should see that the predator lags behind the prey by about 1/4 of a period. Slope field, nullclines, and trajectories: predator-prey model 1 2 3 4 5 6 y 1 2 3 4 5 x Solution curves (prey is red, predator blue) for x(0) = y(0) = 1 1 1.5 2 2.5 3 3.5 y(t) 2 4 6 8 10 12 t Solution curves (prey is red, predator blue) for x(0) = y(0) = 0.4 1 2 3 4 5 6 7 x(t) 2 4 6 8 10 12 t...
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